Question

If 2mi+2mj is a unit vector, then the value of ‘m’ is A. 1/√3 B.1/√2 C.1/√ 5 D.1/2

Answer 1

v = 2m i + 2m j has magnitude |v| = sqrt((2m)^2+(2m)^2) = sqrt(8m^2) = 2√2 |m|.
Setting |v| = 1 gives 2√2 |m| = 1 ⇒ |m| = 1/(2√2) = 1/√8 = √2/4.

So m = ±1/(2√2). If m is taken positive, m = 1/(2√2) (not listed among A–D).