IB Maths AA HL 3.16 Vector product Question Bank

attempt to find cross product (e.g. correct except for sign error)
$\boldsymbol{a} \times \boldsymbol{p}=\left(\begin{array}{c}0 \\ -36 \\ 0\end{array}\right)$

METHOD 1

choosing to use scalar product for their $\boldsymbol{a} \times \boldsymbol{p}$ and $\boldsymbol{a} \times \boldsymbol{n}$$(\boldsymbol{a} \times \boldsymbol{p}) \cdot(\boldsymbol{a} \times \boldsymbol{n})=\mathbf{0}$
so angle is $90^{\circ}$

METHOD 2
$\boldsymbol{a} \times \boldsymbol{n}=\left(\begin{array}{c}0 \\ 0 \\ 36\end{array}\right)$

Note: The final A1 can be awarded for seeing the dot product equals zero without incorrect working. Follow through from (i) is permitted and if they explicitly state that they are using $\boldsymbol{a} \times \boldsymbol{n}$ then allow internal follow through. \\ Note: The final A1 can be awarded for seeing the dot product equals zero
without incorrect working. Follow through from (i) is permitted and if they
explicitly state that they are using $\boldsymbol{a} \times \boldsymbol{n}$ then allow internal follow through.
o angle is $90^{\circ}$
attempt to use cross product for their $\boldsymbol{a} \times \boldsymbol{p}$ and $\boldsymbol{a} \times \boldsymbol{n}$. This must include both an attempt to find the cross product and knowledge that $\sin \theta=\frac{|x \times y|}{|x||y|}$$(\boldsymbol{a} \times \boldsymbol{n}) \times(\boldsymbol{a} \times \boldsymbol{p})=\left(\begin{array}{c}1296 \\ 0 \\ 0\end{array}\right)$ OR $(\boldsymbol{a} \times \boldsymbol{p}) \times(\boldsymbol{a} \times \boldsymbol{n})=\left(\begin{array}{c}-1296 \\ 0 \\ 0\end{array}\right)$$\sin \theta=\frac{1296}{36 \times 36}=1$
so angle is $90^{\circ}$
AG