DP Mathematics HL Questionbank
4.5
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[N/A]Directly related questions
- 17M.2.hl.TZ2.7: Given that a \( \times \) b \( = \) b \( \times \) c \( \ne \) 0 prove that a \( + \) c \( = \)...
- 17M.1.hl.TZ1.5a: Find the area of the parallelogram ABCD.
- 15N.1.hl.TZ0.13d: The coordinates of the points \(A\), \(B\) and \(C\) are \((1,{\text{ }}3,{\text{ }}1)\),...
- 12N.2.hl.TZ0.13d: Determine a Cartesian equation of the plane \({\pi _3}\) containing both lines \({L_1}\) and...
- 08M.1.hl.TZ2.10: Given any two non-zero vectors a and b , show that \(|\)a \( \times \) b\({|^2}\) =...
- 11M.2.hl.TZ2.11b: The vector product...
- 11M.2.hl.TZ2.11c: Hence calculate the area of parallelogram PQRS.
- SPNone.1.hl.TZ0.8: The vectors a , b , c satisfy the equation a + b + c = 0 . Show that a \( \times \) b = b...
- SPNone.2.hl.TZ0.10a: (i) Find \(\overrightarrow {{\text{OA}}} \times \overrightarrow {{\text{OB}}} \) . (ii) ...
- SPNone.2.hl.TZ0.13e: Consider the points \({\text{A}}\left( {a{\text{ }},{\text{ }}f(a)} \right)\) ,...
- 13M.1.hl.TZ1.2b: Hence find the area of the triangle ABC.
- 13M.1.hl.TZ1.2a: Find \(\overrightarrow {{\text{AB}}} \times \overrightarrow {{\text{AC}}} \).
- 10M.1.hl.TZ2.12a: Consider the vectors a = 6i + 3j + 2k, b = −3j + 4k. (i) Find the cosine of the angle...
- 10N.2.hl.TZ0.12: The diagram shows a cube OABCDEFG. Let O be the origin, (OA) the x-axis, (OC) the y-axis...
- 13M.1.hl.TZ2.11b: (i) Show that \(\overrightarrow {{\text{BC}}} \times \overrightarrow {{\text{CA}}} = \) −7i...
- 11N.1.hl.TZ0.12a: For non-zero vectors \({\boldsymbol{a}}\) and \({\boldsymbol{b}}\), show that (i) if...
- 11N.1.hl.TZ0.12b: The points A, B and C have position vectors \({\boldsymbol{a}}\), \({\boldsymbol{b}}\) and...
- 10N.2.hl.TZ0.9: Consider the vectors a \( = \sin (2\alpha )\)i \( - \cos (2\alpha )\)j + k and b...
- 11M.1.hl.TZ1.11b: Find the Cartesian equation of the plane \(\prod \) that contains the face ABC.
- 13N.1.hl.TZ0.11b: Find an exact value for the area of the triangle ABC.
- 13N.1.hl.TZ0.11a: Find the vector \(\overrightarrow {{\text{CA}}} \times \overrightarrow {{\text{CB}}} \).
- 09M.1.hl.TZ1.8: A triangle has vertices A(1, −1, 1), B(1, 1, 0) and C(−1, 1, −1) . Show that the area of the...
- 16M.2.hl.TZ1.1b: Hence find the area of the triangle OAB.
- 16M.2.hl.TZ1.1a: Find \(\overrightarrow {{\text{OA}}} \times \overrightarrow {{\text{OB}}} \).
- 16N.1.hl.TZ0.4a: Find a \( \times \) b.
Sub sections and their related questions
The definition of the vector product of two vectors.
- 12N.2.hl.TZ0.13d: Determine a Cartesian equation of the plane \({\pi _3}\) containing both lines \({L_1}\) and...
- 11M.2.hl.TZ2.11b: The vector product...
- 11M.2.hl.TZ2.11c: Hence calculate the area of parallelogram PQRS.
- SPNone.1.hl.TZ0.8: The vectors a , b , c satisfy the equation a + b + c = 0 . Show that a \( \times \) b = b...
- SPNone.2.hl.TZ0.10a: (i) Find \(\overrightarrow {{\text{OA}}} \times \overrightarrow {{\text{OB}}} \) . (ii) ...
- SPNone.2.hl.TZ0.13e: Consider the points \({\text{A}}\left( {a{\text{ }},{\text{ }}f(a)} \right)\) ,...
- 13M.1.hl.TZ1.2a: Find \(\overrightarrow {{\text{AB}}} \times \overrightarrow {{\text{AC}}} \).
- 13M.1.hl.TZ1.2b: Hence find the area of the triangle ABC.
- 10M.1.hl.TZ2.12a: Consider the vectors a = 6i + 3j + 2k, b = −3j + 4k. (i) Find the cosine of the angle...
- 10N.2.hl.TZ0.9: Consider the vectors a \( = \sin (2\alpha )\)i \( - \cos (2\alpha )\)j + k and b...
- 10N.2.hl.TZ0.12: The diagram shows a cube OABCDEFG. Let O be the origin, (OA) the x-axis, (OC) the y-axis...
- 13M.1.hl.TZ2.11b: (i) Show that \(\overrightarrow {{\text{BC}}} \times \overrightarrow {{\text{CA}}} = \) −7i...
- 11N.1.hl.TZ0.12a: For non-zero vectors \({\boldsymbol{a}}\) and \({\boldsymbol{b}}\), show that (i) if...
- 11N.1.hl.TZ0.12b: The points A, B and C have position vectors \({\boldsymbol{a}}\), \({\boldsymbol{b}}\) and...
- 11M.1.hl.TZ1.11b: Find the Cartesian equation of the plane \(\prod \) that contains the face ABC.
- 13N.1.hl.TZ0.11b: Find an exact value for the area of the triangle ABC.
- 13N.1.hl.TZ0.11a: Find the vector \(\overrightarrow {{\text{CA}}} \times \overrightarrow {{\text{CB}}} \).
- 15N.1.hl.TZ0.13d: The coordinates of the points \(A\), \(B\) and \(C\) are \((1,{\text{ }}3,{\text{ }}1)\),...
- 16M.2.hl.TZ1.1a: Find \(\overrightarrow {{\text{OA}}} \times \overrightarrow {{\text{OB}}} \).
- 16M.2.hl.TZ1.1b: Hence find the area of the triangle OAB.
- 16N.1.hl.TZ0.4a: Find a \( \times \) b.
Properties of the vector product: \({\text{v}} \times {\text{w}} = - {\text{w}} \times {\text{v}}\) ; \({\text{u}} \times ({\text{v}} + {\text{w}}) = {\text{u}} \times {\text{v}} + {\text{u}} \times {\text{w}}\) ; \((k{\text{v}}) \times {\text{w}} = k({\text{v}} + {\text{w}})\) ; \({\text{v}} \times {\text{v}} = 0\) .
- 08M.1.hl.TZ2.10: Given any two non-zero vectors a and b , show that \(|\)a \( \times \) b\({|^2}\) =...
- 16M.2.hl.TZ1.1a: Find \(\overrightarrow {{\text{OA}}} \times \overrightarrow {{\text{OB}}} \).
- 16M.2.hl.TZ1.1b: Hence find the area of the triangle OAB.
- 16N.1.hl.TZ0.4a: Find a \( \times \) b.
