Let a ^ and b ^ are two non-collinear unit vectors. If u → = a ^ - a ^ · b ^ b ^ and v → = a ^ × b ^ , then | v → | is equal to

Step-by-step solution

We have, a ^ = b ^ = 1 Given, v → = a ^ × b ^ = a ^ b ^ sin θ n ^ = sin θ n ^ where, θ is the angle between a ^ and b ^ . ∴       v → = sin θ Now, u → = a ^ - a ^ · b ^ b ^ = a ^ - a ^ b ^ cos θ b ^ u → = a ^ - cos θ b ^ ∴   u → = a ^ 2 + - cos θ b ^ 2 - 2 a ^ - cos θ b ^ cos θ ⇒   u → = 1 + cos 2 θ - 2 cos 2 θ ⇒ u → = 1 - cos 2 θ = sin 2 θ ∴ &#1