DP Mathematics SL Questionbank

• Syllabus

4.2

Sub sections and their related questions

The scalar product of two vectors.

• 12N.1.sl.TZ0.9a: Show that...
• 12N.1.sl.TZ0.9b: Let C and D be points such that ABCD is a rectangle. Given that...
• 12N.1.sl.TZ0.9c: Let C and D be points such that ABCD is a rectangle. Find the coordinates of point C.
• 12N.1.sl.TZ0.9d: Let C and D be points such that ABCD is a rectangle. Find the area of rectangle ABCD.
• 08N.2.sl.TZ0.8c(i) and (ii): (i)     Find \(\overrightarrow {{\rm{AB}}} \bullet \overrightarrow {{\rm{AD}}} \). (ii)    Hence...
• 11M.1.sl.TZ1.9a(i) and (ii): (i)     Write down \(\overrightarrow {{\rm{BA}}} \) . (ii)    Find...
• 11M.1.sl.TZ1.9c(i) and (ii): The point D is such that...
• 13M.2.sl.TZ2.8b: Find the value of \(a\) for which \({\rm{q}} = \frac{\pi }{2}\) .
• 14M.2.sl.TZ1.4b: Given that \(u = \left( \begin{array}{c}3\\2\\1\end{array} \right)\) and...
• 14M.1.sl.TZ2.9c: The position of Jack’s airplane \(s\) seconds after it takes off is given by r =...
• 13N.2.sl.TZ0.9b: Show that the lines are perpendicular.
• 15M.1.sl.TZ1.8d: (i)     Find \(\overrightarrow {{\text{OC}}}  \bullet \overrightarrow {{\text{AB}}} \). (ii)    ...
• 15M.2.sl.TZ2.2a: Find (i)     \(u \bullet v\); (ii)     \(\left| {{u}} \right|\); (iii)    ...
• 16M.2.sl.TZ1.10a: Find \(\overrightarrow {{\text{AB}}} \).
• 16M.2.sl.TZ1.10b: Show that...
• 16M.2.sl.TZ1.10c: Find \(\theta \).
• 16M.2.sl.TZ1.10d: (i)     Show that...
• 16M.1.sl.TZ2.7: Let u \( =  - 3\)i \( + \) j \( + \) k and v \( = m\)j \( + {\text{ }}n\)k , where...
• 16N.1.sl.TZ0.4b: The line through P and Q is perpendicular to the vector 2i \( + \) nk. Find the value of \(n\).
• 17M.1.sl.TZ1.8a.ii: Hence, write down a vector equation for \({L_1}\).
• 17M.1.sl.TZ1.8b: A second line \({L_2}\), has equation r =...
• 17M.1.sl.TZ1.8c: The lines \({L_1}\) and \({L_1}\) intersect at \(C(9,{\text{ }}13,{\text{ }}z)\). Find \(z\).
• 17M.1.sl.TZ1.8d.i: Find a unit vector in the direction of \({L_2}\).
• 17M.1.sl.TZ1.8d.ii: Hence or otherwise, find one point on \({L_2}\) which is \(\sqrt 5 \) units from C.
• 17M.1.sl.TZ2.2a: Find the value of \(k\).
• 17M.1.sl.TZ2.2b: Given that c = a + 2b, find c.
• 17N.1.sl.TZ0.9a.i: Show that...
• 17N.1.sl.TZ0.9a.ii: Find a vector equation for \(L\).
• 17N.1.sl.TZ0.9b: Find the value of \(p\).
• 17N.1.sl.TZ0.9c: The point D has coordinates \(({q^2},{\text{ }}0,{\text{ }}q)\). Given that...
• 18M.1.sl.TZ1.6: Six equilateral triangles, each with side length 3 cm, are arranged to form a hexagon.This is...
• 18M.1.sl.TZ1.9a: Show...
• 18M.1.sl.TZ1.9b.i: Find a vector equation for L.
• 18M.1.sl.TZ1.9b.ii: Point C (k , 12 , −k) is on L. Show that k = 14.
• 18M.1.sl.TZ1.9c.i: Find \(\mathop {{\text{OB}}}\limits^ \to  \, \bullet \mathop {{\text{AB}}}\limits^ \to  \).
• 18M.1.sl.TZ1.9c.ii: Write down the value of angle OBA.
• 18M.1.sl.TZ1.9d: Point D is also on L and has coordinates (8, 4, −9). Find the area of triangle OCD.
• 18M.1.sl.TZ2.1a: Find a vector equation for L1.
• 18M.1.sl.TZ2.1b: The vector \(\left( \begin{gathered} 2 \hfill \\ p \hfill \\ 0 \hfill \\ \end{gathered} \right)\)...

Perpendicular vectors; parallel vectors.

• 12N.1.sl.TZ0.9a: Show that...
• 12N.1.sl.TZ0.9b: Let C and D be points such that ABCD is a rectangle. Given that...
• 12N.1.sl.TZ0.9c: Let C and D be points such that ABCD is a rectangle. Find the coordinates of point C.
• 12N.1.sl.TZ0.9d: Let C and D be points such that ABCD is a rectangle. Find the area of rectangle ABCD.
• 08M.2.sl.TZ1.7: Let  \({\boldsymbol{v}} = 3{\boldsymbol{i}} + 4{\boldsymbol{j}} + {\boldsymbol{k}}\) and...
• 08M.1.sl.TZ2.8b: Show that \(k = 7\) .
• 10N.1.sl.TZ0.8a(i), (ii) and (iii): (i)     Show that...
• 10N.1.sl.TZ0.8b(i) and (ii): The line (AC) has equation \({\boldsymbol{r}} = {\boldsymbol{u}} + s{\boldsymbol{v}}\) . (i)    ...
• 10N.1.sl.TZ0.8c: The lines (AC) and (BD) intersect at the point \({\text{P}}(3{\text{, }}k)\) . Show that...
• 10N.1.sl.TZ0.8d: The lines (AC) and (BD) intersect at the point \({\text{P}}(3{\text{, }}k)\) . Hence find the...
• 10M.1.sl.TZ1.10a: Write down a vector equation for \({L_2}\) in the form...
• 10M.1.sl.TZ1.10b: A third line \({L_3}\) is perpendicular to \({L_1}\) and is represented by...
• 10M.1.sl.TZ1.10c: The lines \({L_1}\) and \({L_3}\) intersect at the point A. Find the coordinates of A.
• 10M.1.sl.TZ1.10d(i) and (ii): The lines \({L_2}\)and \({L_3}\)intersect at point C where...
• 10M.1.sl.TZ2.2a: Find \(\overrightarrow {{\rm{BC}}} \) .
• 10M.1.sl.TZ2.2b: Find a unit vector in the direction of \(\overrightarrow {{\rm{AB}}} \) .
• 10M.1.sl.TZ2.2c: Show that \(\overrightarrow {{\rm{AB}}} \) is perpendicular to \(\overrightarrow {{\rm{AC}}} \) .
• 09N.1.sl.TZ0.2a: Let u \( = \left( {\begin{array}{*{20}{c}}2\\3\\{ - 1}\end{array}} \right)\) and w...
• SPNone.2.sl.TZ0.4a: Write down the line that is parallel to \({L_4}\) .
• SPNone.2.sl.TZ0.4c: Given that \({L_1}\) is perpendicular to \({L_3}\) , find the value of a .
• 11N.1.sl.TZ0.8a(i) and (ii): (i)     Find \(\overrightarrow {{\rm{PQ}}} \) . (ii)    Hence write down a vector equation for...
• 11N.1.sl.TZ0.8b(i) and (ii): (i)     Find the value of p . (ii)    Given that \({L_2}\) passes through...
• 11N.1.sl.TZ0.8c: The lines \({L_1}\) and \({L_2}\) intersect at the point A. Find the x-coordinate of A.
• 11M.1.sl.TZ1.9a(i) and (ii): (i)     Write down \(\overrightarrow {{\rm{BA}}} \) . (ii)    Find...
• 11M.1.sl.TZ1.9b(i) and (ii): (i)     Find \(\cos {\rm{A}}\widehat {\rm{B}}{\rm{C}}\) . (ii)    Hence, find...
• 11M.1.sl.TZ1.9c(i) and (ii): The point D is such that...
• 11M.1.sl.TZ2.3a: Find \(\overrightarrow {{\rm{BC}}} \) .
• 11M.1.sl.TZ2.3b: Show...
• 11M.1.sl.TZ2.3c: Show that vectors \(\overrightarrow {{\rm{BD}}} \) and \(\overrightarrow {{\rm{AC}}} \) are...
• 13M.1.sl.TZ1.8b: Given that \({L_1}\) is perpendicular to \({L_2}\) , show that \(p = - 6\) .
• 14M.2.sl.TZ1.4b: Given that \(u = \left( \begin{array}{c}3\\2\\1\end{array} \right)\) and...
• 14M.1.sl.TZ2.4a: Find the gradient of the line \(L\).
• 14M.1.sl.TZ2.9c: The position of Jack’s airplane \(s\) seconds after it takes off is given by r =...
• 13N.2.sl.TZ0.9b: Show that the lines are perpendicular.
• 18M.1.sl.TZ1.9a: Show...
• 18M.1.sl.TZ1.9b.i: Find a vector equation for L.
• 18M.1.sl.TZ1.9b.ii: Point C (k , 12 , −k) is on L. Show that k = 14.
• 18M.1.sl.TZ1.9c.i: Find \(\mathop {{\text{OB}}}\limits^ \to  \, \bullet \mathop {{\text{AB}}}\limits^ \to  \).
• 18M.1.sl.TZ1.9c.ii: Write down the value of angle OBA.
• 18M.1.sl.TZ1.9d: Point D is also on L and has coordinates (8, 4, −9). Find the area of triangle OCD.

The angle between two vectors.

• 08N.2.sl.TZ0.8c(i) and (ii): (i)     Find \(\overrightarrow {{\rm{AB}}} \bullet \overrightarrow {{\rm{AD}}} \). (ii)    Hence...
• 08M.2.sl.TZ1.9a(i) and (ii): (i)     Show that...
• 08M.1.sl.TZ2.8d: Find \(\cos {\rm{A}}\widehat {\rm{B}}{\rm{C}}\) .
• 09N.2.sl.TZ0.10e: Let \(\theta \) be the obtuse angle between \({L_1}\) and \({L_2}\) . Calculate the size of...
• 09M.1.sl.TZ1.9b: Show that \(\cos {\rm{R}}\widehat {\rm{P}}{\rm{Q}} = \frac{1}{2}\) .
• 09M.1.sl.TZ2.2: Find the cosine of the angle between the two vectors...
• 10N.2.sl.TZ0.4: Let \({\boldsymbol{v}} = \left( {\begin{array}{*{20}{c}}2\\{ - 3}\\6\end{array}} \right)\) and ...
• 11M.1.sl.TZ1.9a(i) and (ii): (i)     Write down \(\overrightarrow {{\rm{BA}}} \) . (ii)    Find...
• 11M.1.sl.TZ1.9b(i) and (ii): (i)     Find \(\cos {\rm{A}}\widehat {\rm{B}}{\rm{C}}\) . (ii)    Hence, find...
• 11M.1.sl.TZ1.9c(i) and (ii): The point D is such that...
• 13M.2.sl.TZ2.8b: Find the value of \(a\) for which \({\rm{q}} = \frac{\pi }{2}\) .
• 13M.2.sl.TZ2.8c: i. Show that \(\cos q = \frac{{2a + 14}}{{\sqrt {14{a^2} + 280} }}\) . ii. Hence, find the value...
• 14N.1.sl.TZ0.7: The following diagram shows triangle \(ABC\). Let...
• 15M.1.sl.TZ1.8d: (i)     Find \(\overrightarrow {{\text{OC}}}  \bullet \overrightarrow {{\text{AB}}} \). (ii)    ...
• 15M.2.sl.TZ2.2b: Find the angle between \({{u}}\) and \({{v}}\).
• 15N.1.sl.TZ0.9c: A point \(D\) lies on line \({L_2}\) so that...
• 16M.2.sl.TZ1.10a: Find \(\overrightarrow {{\text{AB}}} \).
• 16M.2.sl.TZ1.10b: Show that...
• 16M.2.sl.TZ1.10c: Find \(\theta \).
• 16M.2.sl.TZ1.10d: (i)     Show that...
• 17N.2.sl.TZ0.3a: Find \(\left| {\overrightarrow {{\text{AB}}} } \right|\).
• 17N.2.sl.TZ0.3b: Let ...
• 18M.1.sl.TZ1.9a: Show...
• 18M.1.sl.TZ1.9b.i: Find a vector equation for L.
• 18M.1.sl.TZ1.9b.ii: Point C (k , 12 , −k) is on L. Show that k = 14.
• 18M.1.sl.TZ1.9c.i: Find \(\mathop {{\text{OB}}}\limits^ \to  \, \bullet \mathop {{\text{AB}}}\limits^ \to  \).
• 18M.1.sl.TZ1.9c.ii: Write down the value of angle OBA.
• 18M.1.sl.TZ1.9d: Point D is also on L and has coordinates (8, 4, −9). Find the area of triangle OCD.
• 18M.2.sl.TZ2.8a.i: Find \(\mathop {{\text{PQ}}}\limits^ \to  \).
• 18M.2.sl.TZ2.8a.ii: Find \(\left| {\mathop {{\text{PQ}}}\limits^ \to  } \right|\).
• 18M.2.sl.TZ2.8b: Find the angle between PQ and PR.
• 18M.2.sl.TZ2.8c: Find the area of triangle PQR.
• 18M.2.sl.TZ2.8d: Hence or otherwise find the shortest distance from R to the line through P and Q.