Let \(\vec a\) be a non-zero vector of magnitude 'a' and \(\lambda\) is a non-zero scalar, then \(\lambda\vec a\) is a unit vector if
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(a=\displaystyle\frac{1}{|\lambda|}\)
A unit vector has magnitude 1, and \(|\lambda\vec a| = |\lambda|\,|\vec a|\):
\(|\lambda\vec a| = 1\)
\(|\lambda|\,a = 1\)
\( \displaystyle a = \frac{1}{|\lambda|} \)
(With \(\lambda = \pm 1\), \(|\lambda\vec a| = a\), which is 1 only when \(\vec a\) itself is a unit vector.)
NCERT (2026-27 edition):
Product of Two Vectors
