Question

If the angle between the vectors $\hat{i}-m\hat{j}$ and $\hat{j}+\hat{k}$ is $\frac{\pi }{3}$, then what is the value of $m$?

• A. $0$
• B. $2$
• C. $-2$
• D. None of the above

Answer 1

The correct option is D None of the above

Dot product of two vectors $a,b$ is $a.b=|a||b|\cos A$ where $A$ is the angle between two vectors.

So, $(\hat{i}-m\hat{j}).(\hat{j}+\hat{k})=\sqrt{1^2+{(-m)}^2}\sqrt{1^2+1^2}\cos \left(\frac{\pi }{3}\right)$

$\Rightarrow -m=\sqrt{1+{\left(m\right)}^2}\sqrt{2}\times \frac{1}{2}\Rightarrow 2m^2=1+m^2\Rightarrow m=\pm 1$