Question

The angle between two vectors $\overrightarrow{R} = -\hat{i} + \frac{1}{3}\hat{j} + \hat{k}$ and $\overrightarrow{S} = x\hat{i} + 3\hat{j} + (x-1)\hat{k}$

• A. Is obtuse angle
• B. Is acute angle
• C. Lies between 60° and 120°
• D. Depends on x

Answer 1

Answer: (C)

Lies between 60° and 120°

Answer 2

Calculate the dot product of the two vectors:

$\overrightarrow{R} \cdot \overrightarrow{S} = (-\hat{i} + \frac{1}{3}\hat{j} + \hat{k}) \cdot (x\hat{i} + 3\hat{j} + (x-1)\hat{k}) = -x + 1 + x - 1 = 0$

Since the dot product is 0, the angle between the vectors is $90^\circ$. A $90^\circ$ angle lies between $60^\circ$ and $120^\circ$.