Question

If length each sides of cube is one unit, then shortest distance between diagonal vector OO' and one edge AB' which is non-co-planer to vector OO' is ____

(A) (1/2)

(B) (1/√2)

(C) √2

(d) 2

Answer 1

The correct option  (B) (1/√2)  

Explanation:

equation of vector OO' (x/1) = (y/1) = (z/1)

equation of vector AB' [(x – 1)/0] = (y/0) = (z/1)

∴ vector a = (0, 0, 0) and b = (1, 0, 0)

also vector ℓ = (1, 1, 1) and m = (0, 0, 1)

∴ vector b – vector a = (1, 0, 0)

vector l x vector m

∴ vector (b – a) ∙ vector (ℓ × m) = (1, 0, 0) ∙ (1, – 1, 0) = 1 

∴ vector |ℓ × m| = √(1 + 1 + 0) = √2

shortest distance between skew lines = (1/√2).