Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Vectors

Question:

If \(\vec{a}\) is a nonzero vector of magnitude \(a\) and \(\lambda\) is a nonzero scalar, then \(\lambda \vec{a}\) is unit vector if

Options:

\(\lambda=1\)

\(\lambda=-1\)

\(a=\left|\lambda\right|\)

\(a=\frac{1}{\left|\lambda \right|}\)

Correct Answer:

\(a=\frac{1}{\left|\lambda \right|}\)

Explanation:
\(\begin{aligned}|\lambda \vec{a}|&=1\\ |\lambda ||\vec{a}|&=1\\ |\vec{a}|&=\frac{1}{|\lambda|}\end{aligned}\)