Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Vectors

Question:

If \(\vec{a}\) and \(\vec{b}\) are unit vectors such that \(\vec{a}\cdot \vec{b}=\cos \theta\) then the value of \(\left|\vec{a}+\vec{b}\right|\) is

Options:

\(2\sin \left(\frac{\theta}{2}\right)\)

\(2\sin \theta\)

\(2\cos \left(\frac{\theta}{2}\right)\)

\(2\cos \theta\)

Correct Answer:

\(2\cos \left(\frac{\theta}{2}\right)\)

Explanation:
\(\begin{aligned}|\vec{a}+\vec{b}|^{2}&=1+1+2\cos \theta\\ &=2(1+\cos \theta)\\ &=4\cos^{2}\frac{\theta}{2}\\ |\vec{a}+\vec{b}|&=2\cos \left(\frac{\theta}{2}\right)\end{aligned}\)