Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Vectors

Question:

Let \(\vec{a}\) and \(\vec{b}\) be two unit vectors and \(\theta\) is the angle between them. Then \(\vec{a}+\vec{b}\) is a unit vector of

Options:

\(\theta=\frac{\pi}{4}\)

\(\theta=\frac{\pi}{3}\)

\(\theta=\frac{\pi}{2}\)

\(\theta=\frac{2\pi}{3}\)

Correct Answer:

\(\theta=\frac{2\pi}{3}\)

Explanation:
\(\begin{aligned}|\vec{a}+\vec{b}|^{2}&=1\\ 1+1+2\cos \theta&=1\\ \cos \theta&=-1\\ \theta &=\frac{2\pi}{3}\end{aligned}\)