DP Mathematics HL Questionbank
4.1
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[N/A]Directly related questions
- 17N.1.hl.TZ0.9e: Given that area ΔOAB=k(area ΔCAD), find the value of...
- 17N.1.hl.TZ0.9d: Deduce an expression for →CD in terms of a and b only.
- 17N.1.hl.TZ0.9c: Show that μ=113, and find the value of λ.
- 17N.1.hl.TZ0.9b.ii: Find an expression for →OD in terms of a, b and μ.
- 17N.1.hl.TZ0.9b.i: Find an expression for →OD in terms of a, b and λ;
- 17N.1.hl.TZ0.9a.ii: Find, in terms of a and b →AF.
- 17N.1.hl.TZ0.9a.i: Find, in terms of a and b →OF.
- 15N.2.hl.TZ0.10a: find the vectors a and b.
- 15N.1.hl.TZ0.13a: Find →BR in terms of a, b and c.
- 11M.1.hl.TZ2.6a: Find an expression for →CB and for...
- 11M.2.hl.TZ2.11a: Find the coordinates of S.
- SPNone.2.hl.TZ0.8a: Show that OC = 2AB .
- SPNone.2.hl.TZ0.8b: Find the position vectors of C, D and E in terms of a and b .
- 10M.1.hl.TZ2.3: The three vectors \boldsymbol{a}, \boldsymbol{b} and \boldsymbol{c} are given...
- 10N.1.hl.TZ0.10: Let \alpha be the angle between the unit vectors a and b, where...
- 13M.1.hl.TZ2.11a: (i) Find the lengths of the sides of the triangle. (ii) Find \cos {\rm{B\hat AC}}.
- 11M.1.hl.TZ1.4a: Write down expressions for \overrightarrow {{\text{AB}}} and...
- 11M.1.hl.TZ1.11a: Find the vectors \overrightarrow {{\text{AB}}} and \overrightarrow {{\text{AC}}} .
- 14M.1.hl.TZ1.12b: Find the coordinates of M, the mid-point of [OB].
- 18M.1.hl.TZ2.9c: Find the area of the parallelogram ABCD.
- 18M.1.hl.TZ2.9b: Show that p = 1, q = 1 and r = 4.
- 18M.1.hl.TZ2.9a.ii: Using vector algebra, show that...
- 18M.1.hl.TZ2.9a.i: Explain why ABCD is a parallelogram.
- 18M.2.hl.TZ1.11b.ii: Find the value of t when submarine B passes through P.
- 18M.2.hl.TZ1.11b.i: Show that submarine B travels in the same direction as originally planned.
- 18M.2.hl.TZ1.11a: Show that the two submarines would collide at a point P and write down the coordinates of P.
- 16M.2.hl.TZ2.9b: Given that...
- 16M.2.hl.TZ2.9a: Show that (i) {\left| {\overrightarrow {{\text{OC}}} } \right|^2} = |a\({|^2} +...
- 16M.1.hl.TZ1.8: O, A, B and C are distinct points such that \overrightarrow {{\text{OA}}} = a,...
- 14M.1.hl.TZ2.6: PQRS is a rhombus. Given that \overrightarrow {{\text{PQ}}} = \boldsymbol{a} and...
- 14M.1.hl.TZ1.12a: Show that the points {\text{O}}(0,{\text{ }}0,{\text{ }}0),...
- 15M.2.hl.TZ2.11c: Find the distance between the two points on the curve where each tangent is parallel to the line...
- 14N.1.hl.TZ0.3: A point P, relative to an origin O, has position vector...
- 14N.1.hl.TZ0.12a: (i) Express \overrightarrow {{\text{AM}}} in terms of a and c. (ii) Hence...
- 14N.1.hl.TZ0.12b: (i) Express \overrightarrow {{\text{RA}}} in terms of a and b. (ii) Show...
- 14N.1.hl.TZ0.12c: Prove that T lies on [BM].
Sub sections and their related questions
Concept of a vector.
- 11M.1.hl.TZ2.6a: Find an expression for \overrightarrow {{\text{CB}}} and for...
- 11M.2.hl.TZ2.11a: Find the coordinates of S.
- SPNone.2.hl.TZ0.8a: Show that OC = 2AB .
- SPNone.2.hl.TZ0.8b: Find the position vectors of C, D and E in terms of a and b .
- 13M.1.hl.TZ2.11a: (i) Find the lengths of the sides of the triangle. (ii) Find \cos {\rm{B\hat AC}}.
- 11M.1.hl.TZ1.4a: Write down expressions for \overrightarrow {{\text{AB}}} and...
- 11M.1.hl.TZ1.11a: Find the vectors \overrightarrow {{\text{AB}}} and \overrightarrow {{\text{AC}}} .
- 18M.2.hl.TZ1.11a: Show that the two submarines would collide at a point P and write down the coordinates of P.
Representation of vectors using directed line segments.
- 11M.1.hl.TZ2.6a: Find an expression for \overrightarrow {{\text{CB}}} and for...
- 18M.2.hl.TZ1.11a: Show that the two submarines would collide at a point P and write down the coordinates of P.
Unit vectors; base vectors i, j, k.
- 11M.1.hl.TZ2.6a: Find an expression for \overrightarrow {{\text{CB}}} and for...
- 18M.2.hl.TZ1.11a: Show that the two submarines would collide at a point P and write down the coordinates of P.
Components of a vector: v = \left( {\begin{array}{*{20}{c}} {{v_1}} \\ {{v_2}} \\ {{v_3}} \end{array}} \right) = {v_1}i + {v_2}j + {v_3}k .
- 11M.1.hl.TZ2.6a: Find an expression for \overrightarrow {{\text{CB}}} and for...
- 18M.2.hl.TZ1.11a: Show that the two submarines would collide at a point P and write down the coordinates of P.
Algebraic and geometric approaches to the sum and difference of two vectors.
- 11M.1.hl.TZ2.6a: Find an expression for \overrightarrow {{\text{CB}}} and for...
- 10M.1.hl.TZ2.3: The three vectors \boldsymbol{a}, \boldsymbol{b} and \boldsymbol{c} are given...
- 10N.1.hl.TZ0.10: Let \alpha be the angle between the unit vectors a and b, where...
- 14M.1.hl.TZ1.12b: Find the coordinates of M, the mid-point of [OB].
- 14M.1.hl.TZ2.6: PQRS is a rhombus. Given that \overrightarrow {{\text{PQ}}} = \boldsymbol{a} and...
- 14M.1.hl.TZ1.12a: Show that the points {\text{O}}(0,{\text{ }}0,{\text{ }}0),...
- 15N.1.hl.TZ0.13a: Find \overrightarrow {{\text{BR}}} in terms of {{a}}, {{b}} and {{c}}.
- 15N.2.hl.TZ0.10a: find the vectors {{a}} and {{b}}.
- 16M.1.hl.TZ1.8: O, A, B and C are distinct points such that \overrightarrow {{\text{OA}}} = a,...
- 16M.2.hl.TZ2.9a: Show that (i) {\left| {\overrightarrow {{\text{OC}}} } \right|^2} = |a\({|^2} +...
- 16M.2.hl.TZ2.9b: Given that...
- 17N.1.hl.TZ0.9a.i: Find, in terms of a and b \overrightarrow {{\text{OF}}} .
- 17N.1.hl.TZ0.9a.ii: Find, in terms of a and b \overrightarrow {{\text{AF}}} .
- 17N.1.hl.TZ0.9b.i: Find an expression for \overrightarrow {{\text{OD}}} in terms of a, b and \lambda ;
- 17N.1.hl.TZ0.9b.ii: Find an expression for \overrightarrow {{\text{OD}}} in terms of a, b and \mu .
- 17N.1.hl.TZ0.9c: Show that \mu = \frac{1}{{13}}, and find the value of \lambda .
- 17N.1.hl.TZ0.9d: Deduce an expression for \overrightarrow {{\text{CD}}} in terms of a and b only.
- 17N.1.hl.TZ0.9e: Given that area \Delta {\text{OAB}} = k({\text{area }}\Delta {\text{CAD}}), find the value of...
- 18M.1.hl.TZ2.9a.i: Explain why ABCD is a parallelogram.
- 18M.1.hl.TZ2.9a.ii: Using vector algebra, show that...
- 18M.1.hl.TZ2.9b: Show that p = 1, q = 1 and r = 4.
- 18M.1.hl.TZ2.9c: Find the area of the parallelogram ABCD.
Algebraic and geometric approaches to the zero vector 0, the vector - v .
- 11M.1.hl.TZ2.6a: Find an expression for \overrightarrow {{\text{CB}}} and for...
- 14M.1.hl.TZ1.12b: Find the coordinates of M, the mid-point of [OB].
- 14M.1.hl.TZ2.6: PQRS is a rhombus. Given that \overrightarrow {{\text{PQ}}} = \boldsymbol{a} and...
- 14M.1.hl.TZ1.12a: Show that the points {\text{O}}(0,{\text{ }}0,{\text{ }}0),...
- 16M.1.hl.TZ1.8: O, A, B and C are distinct points such that \overrightarrow {{\text{OA}}} = a,...
- 16M.2.hl.TZ2.9a: Show that (i) {\left| {\overrightarrow {{\text{OC}}} } \right|^2} = |a\({|^2} +...
- 16M.2.hl.TZ2.9b: Given that...
- 17N.1.hl.TZ0.9a.i: Find, in terms of a and b \overrightarrow {{\text{OF}}} .
- 17N.1.hl.TZ0.9a.ii: Find, in terms of a and b \overrightarrow {{\text{AF}}} .
- 17N.1.hl.TZ0.9b.i: Find an expression for \overrightarrow {{\text{OD}}} in terms of a, b and \lambda ;
- 17N.1.hl.TZ0.9b.ii: Find an expression for \overrightarrow {{\text{OD}}} in terms of a, b and \mu .
- 17N.1.hl.TZ0.9c: Show that \mu = \frac{1}{{13}}, and find the value of \lambda .
- 17N.1.hl.TZ0.9d: Deduce an expression for \overrightarrow {{\text{CD}}} in terms of a and b only.
- 17N.1.hl.TZ0.9e: Given that area \Delta {\text{OAB}} = k({\text{area }}\Delta {\text{CAD}}), find the value of...
- 18M.1.hl.TZ2.9a.i: Explain why ABCD is a parallelogram.
- 18M.1.hl.TZ2.9a.ii: Using vector algebra, show that...
- 18M.1.hl.TZ2.9b: Show that p = 1, q = 1 and r = 4.
- 18M.1.hl.TZ2.9c: Find the area of the parallelogram ABCD.
Algebraic and geometric approaches to multiplication by a scalar, kv .
- 11M.1.hl.TZ2.6a: Find an expression for \overrightarrow {{\text{CB}}} and for...
- 14M.1.hl.TZ1.12b: Find the coordinates of M, the mid-point of [OB].
- 14M.1.hl.TZ2.6: PQRS is a rhombus. Given that \overrightarrow {{\text{PQ}}} = \boldsymbol{a} and...
- 14M.1.hl.TZ1.12a: Show that the points {\text{O}}(0,{\text{ }}0,{\text{ }}0),...
- 15N.1.hl.TZ0.13a: Find \overrightarrow {{\text{BR}}} in terms of {{a}}, {{b}} and {{c}}.
- 15N.2.hl.TZ0.10a: find the vectors {{a}} and {{b}}.
- 16M.1.hl.TZ1.8: O, A, B and C are distinct points such that \overrightarrow {{\text{OA}}} = a,...
- 16M.2.hl.TZ2.9a: Show that (i) {\left| {\overrightarrow {{\text{OC}}} } \right|^2} = |a\({|^2} +...
- 16M.2.hl.TZ2.9b: Given that...
- 17N.1.hl.TZ0.9a.i: Find, in terms of a and b \overrightarrow {{\text{OF}}} .
- 17N.1.hl.TZ0.9a.ii: Find, in terms of a and b \overrightarrow {{\text{AF}}} .
- 17N.1.hl.TZ0.9b.i: Find an expression for \overrightarrow {{\text{OD}}} in terms of a, b and \lambda ;
- 17N.1.hl.TZ0.9b.ii: Find an expression for \overrightarrow {{\text{OD}}} in terms of a, b and \mu .
- 17N.1.hl.TZ0.9c: Show that \mu = \frac{1}{{13}}, and find the value of \lambda .
- 17N.1.hl.TZ0.9d: Deduce an expression for \overrightarrow {{\text{CD}}} in terms of a and b only.
- 17N.1.hl.TZ0.9e: Given that area \Delta {\text{OAB}} = k({\text{area }}\Delta {\text{CAD}}), find the value of...
- 18M.1.hl.TZ2.9a.i: Explain why ABCD is a parallelogram.
- 18M.1.hl.TZ2.9a.ii: Using vector algebra, show that...
- 18M.1.hl.TZ2.9b: Show that p = 1, q = 1 and r = 4.
- 18M.1.hl.TZ2.9c: Find the area of the parallelogram ABCD.
Algebraic and geometric approaches to magnitude of a vector, \left| v \right| .
- 11M.1.hl.TZ2.6a: Find an expression for \overrightarrow {{\text{CB}}} and for...
- 10M.1.hl.TZ2.3: The three vectors \boldsymbol{a}, \boldsymbol{b} and \boldsymbol{c} are given...
- 10N.1.hl.TZ0.10: Let \alpha be the angle between the unit vectors a and b, where...
- 14M.1.hl.TZ1.12b: Find the coordinates of M, the mid-point of [OB].
- 14M.1.hl.TZ2.6: PQRS is a rhombus. Given that \overrightarrow {{\text{PQ}}} = \boldsymbol{a} and...
- 14M.1.hl.TZ1.12a: Show that the points {\text{O}}(0,{\text{ }}0,{\text{ }}0),...
- 14N.1.hl.TZ0.3: A point P, relative to an origin O, has position vector...
- 16M.1.hl.TZ1.8: O, A, B and C are distinct points such that \overrightarrow {{\text{OA}}} = a,...
- 16M.2.hl.TZ2.9a: Show that (i) {\left| {\overrightarrow {{\text{OC}}} } \right|^2} = |a\({|^2} +...
- 16M.2.hl.TZ2.9b: Given that...
- 17N.1.hl.TZ0.9a.i: Find, in terms of a and b \overrightarrow {{\text{OF}}} .
- 17N.1.hl.TZ0.9a.ii: Find, in terms of a and b \overrightarrow {{\text{AF}}} .
- 17N.1.hl.TZ0.9b.i: Find an expression for \overrightarrow {{\text{OD}}} in terms of a, b and \lambda ;
- 17N.1.hl.TZ0.9b.ii: Find an expression for \overrightarrow {{\text{OD}}} in terms of a, b and \mu .
- 17N.1.hl.TZ0.9c: Show that \mu = \frac{1}{{13}}, and find the value of \lambda .
- 17N.1.hl.TZ0.9d: Deduce an expression for \overrightarrow {{\text{CD}}} in terms of a and b only.
- 17N.1.hl.TZ0.9e: Given that area \Delta {\text{OAB}} = k({\text{area }}\Delta {\text{CAD}}), find the value of...
- 18M.1.hl.TZ2.9a.i: Explain why ABCD is a parallelogram.
- 18M.1.hl.TZ2.9a.ii: Using vector algebra, show that...
- 18M.1.hl.TZ2.9b: Show that p = 1, q = 1 and r = 4.
- 18M.1.hl.TZ2.9c: Find the area of the parallelogram ABCD.
Algebraic and geometric approaches to position vectors \overrightarrow {OA} = a .
- 11M.1.hl.TZ2.6a: Find an expression for \overrightarrow {{\text{CB}}} and for...
- 14M.1.hl.TZ1.12b: Find the coordinates of M, the mid-point of [OB].
- 14M.1.hl.TZ2.6: PQRS is a rhombus. Given that \overrightarrow {{\text{PQ}}} = \boldsymbol{a} and...
- 14M.1.hl.TZ1.12a: Show that the points {\text{O}}(0,{\text{ }}0,{\text{ }}0),...
- 14N.1.hl.TZ0.12a: (i) Express \overrightarrow {{\text{AM}}} in terms of a and c. (ii) Hence...
- 14N.1.hl.TZ0.12b: (i) Express \overrightarrow {{\text{RA}}} in terms of a and b. (ii) Show...
- 14N.1.hl.TZ0.12c: Prove that T lies on [BM].
- 15N.1.hl.TZ0.13a: Find \overrightarrow {{\text{BR}}} in terms of {{a}}, {{b}} and {{c}}.
- 16M.1.hl.TZ1.8: O, A, B and C are distinct points such that \overrightarrow {{\text{OA}}} = a,...
- 16M.2.hl.TZ2.9a: Show that (i) {\left| {\overrightarrow {{\text{OC}}} } \right|^2} = |a\({|^2} +...
- 16M.2.hl.TZ2.9b: Given that...
- 17N.1.hl.TZ0.9a.i: Find, in terms of a and b \overrightarrow {{\text{OF}}} .
- 17N.1.hl.TZ0.9a.ii: Find, in terms of a and b \overrightarrow {{\text{AF}}} .
- 17N.1.hl.TZ0.9b.i: Find an expression for \overrightarrow {{\text{OD}}} in terms of a, b and \lambda ;
- 17N.1.hl.TZ0.9b.ii: Find an expression for \overrightarrow {{\text{OD}}} in terms of a, b and \mu .
- 17N.1.hl.TZ0.9c: Show that \mu = \frac{1}{{13}}, and find the value of \lambda .
- 17N.1.hl.TZ0.9d: Deduce an expression for \overrightarrow {{\text{CD}}} in terms of a and b only.
- 17N.1.hl.TZ0.9e: Given that area \Delta {\text{OAB}} = k({\text{area }}\Delta {\text{CAD}}), find the value of...
- 18M.1.hl.TZ2.9a.i: Explain why ABCD is a parallelogram.
- 18M.1.hl.TZ2.9a.ii: Using vector algebra, show that...
- 18M.1.hl.TZ2.9b: Show that p = 1, q = 1 and r = 4.
- 18M.1.hl.TZ2.9c: Find the area of the parallelogram ABCD.
\overrightarrow {AB} = b - a .
- 11M.1.hl.TZ2.6a: Find an expression for \overrightarrow {{\text{CB}}} and for...
- 14N.1.hl.TZ0.12a: (i) Express \overrightarrow {{\text{AM}}} in terms of a and c. (ii) Hence...
- 14N.1.hl.TZ0.12b: (i) Express \overrightarrow {{\text{RA}}} in terms of a and b. (ii) Show...
- 14N.1.hl.TZ0.12c: Prove that T lies on [BM].
- 15M.2.hl.TZ2.11c: Find the distance between the two points on the curve where each tangent is parallel to the line...
- 15N.1.hl.TZ0.13a: Find \overrightarrow {{\text{BR}}} in terms of {{a}}, {{b}} and {{c}}.
- 17N.1.hl.TZ0.9a.ii: Find, in terms of a and b \overrightarrow {{\text{AF}}} .