DP Mathematics HL Questionbank

• Syllabus

4.5

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.

Geometric interpretation of ${\text{v}} \times {\text{w}}$ .

• 10N.2.hl.TZ0.12: The diagram shows a cube OABCDEFG.     Let O be the origin, (OA) the x-axis, (OC) the y-axis...
• 15N.1.hl.TZ0.13d: The coordinates of the points $A$, $B$ and $C$ are $(1,{\text{ }}3,{\text{ }}1)$,...