Question

The angle between two vectors $\vec{i} + \vec{j}$ and $\vec{j} + \vec{k}$ is

• A. $60^\circ$
• B. $30^\circ$
• C. $45^\circ$
• D. $90^\circ$

Hint:

Use the dot product formula to find the angle between two vectors: $\cos \theta = \dfrac{\vec{A} \cdot \vec{B}}{|\vec{A}| |\vec{B}|}$

Answer 1

The Correct Option is A

Let $\vec{A} = \hat{i} + \hat{j}$ and $\vec{B} = \hat{j} + \hat{k}$.
Dot product: $\vec{A} \cdot \vec{B} = (1)(0) + (1)(1) + (0)(1) = 1$
$|\vec{A}| = \sqrt{1^2 + 1^2} = \sqrt{2}$, $|\vec{B}| = \sqrt{1^2 + 1^2} = \sqrt{2}$
So, $\cos \theta = \dfrac{\vec{A} \cdot \vec{B}}{|\vec{A}| |\vec{B}|} = \dfrac{1}{2} \Rightarrow \theta = 60^\circ$