Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Vectors

Question:
If the sum of two unit vectors is a unit vector, then angle between them is
Options:
\(\frac{\pi}{3}\)
\(\frac{\pi}{4}\)
\(\frac{3\pi}{4}\)
\(\frac{2\pi}{3}\)
Correct Answer:
\(\frac{2\pi}{3}\)
Explanation:
Let , \(|\vec{a}|=1,|\vec{b}|=1,|\vec{a}+\vec{b}|=1\) then \(|\vec{a}+\vec{b}|^2=1\hspace{7 cm}\) \(\begin{aligned}|a|^{2}+|b|^{2}+2|a||b|\cos \theta &=1\\ \cos \theta &=\frac{1}{2}\\ \theta&=120\end{aligned}\)