Q11 (b)

Criteria	Marks
Provides correct solution	3
Correctly evaluates $\vec a\cdot\vec b$ and $	\vec a
Evaluates $\vec a\cdot\vec b$ or $	\vec a

Sample answer:

$\vec a\cdot\vec b=(1\times(-1))+(2\times4)+(-3\times2)$
$=-1+8-6=1$
$|\vec a|=\sqrt{1^2+2^2+(-3)^2}=\sqrt{14}$
$|\vec b|=\sqrt{(-1)^2+4^2+2^2}=\sqrt{21}$
$\vec a\cdot\vec b=|\vec a||\vec b|\cos\theta$
$\therefore\cos\theta=\frac{1}{\sqrt{14}\cdot\sqrt{21}}$
$\theta=\cos^{-1}\left(\frac{1}{\sqrt{14}\cdot\sqrt{21}}\right)=86.656\ldots\approx87^\circ\ \text{(nearest degree)}$