Question

Angle between vectors $\left(\hat{i}+\hat{j}\right)$ and $\left(\hat{j}+\hat{k}\right)$ is

• A. $30^{°}$
• B. $45^{°}$
• C. $60^{°}$
• D. $90^{°}$

Answer 1

Answer: (C)

Let $\vec{A}=\hat{i}+\hat{j}$ and $\vec{B}=\hat{j}+\hat{k}$ and $\theta$ is the angle between them
Also, $\left|\vec{A}\right|=\sqrt{{\left(1\right)}^2+{\left(1\right)}^2}=\sqrt{2}$;
$\left|\vec{B}\right|=\sqrt{{\left(1\right)}^2+{\left(1\right)}^2}=\sqrt{2}$;
$\left|\vec{B}\right|=\sqrt{{\left(1\right)}^2+{\left(1\right)}^2}=\sqrt{2}$
$\therefore \vec{A}\cdot \vec{B}=\left|\vec{A}\right|\left|\vec{B}\right|cos\theta$
$\left(\hat{i}+\hat{j}\right)\cdot \left(\hat{j}+\hat{k}\right)=\sqrt{2}\sqrt{2}cos\theta$
$\left[0+0+1+0\right]=2cos\theta$
or $cos\theta =\frac{1}{2}$ or $\theta =co{s}^{-1}\left(\frac{1}{2}\right)$
or $\theta =60^{\circ }$