Question

If $\vec a$ is a nonzero vector of magnitude ‘a’ and λ a nonzero scalar, then λ $\vec a$ is unit vector if
(A) λ = 1
(B) λ = - 1
(C) a = |λ |
(D) a = 1/| λ|

Answer 1

It is given that there is one vector a whose magnitude is a, where a ≠ 0,

and if it is multiplied with scalar λ which is non-zero, then,

λa = λ × a

Now, As per as Question, λ  when multiplied with a will give an unit vector.

Unit vector have magnitude of 1.

∴ λa = 1

∴ a = 1/λ

Now, magnitude of vector a can never be negative.

Therefore, a = 1/|λ|

Hence, option (D). is correct.

Hope it helps.