Question

Find the angle between the vectors `vec"a" + vec"b" and  vec"a" -vec"b" if  vec"a" = 2hat"i"-hat"j"+3hat"k" and vec"b" = 3hat"i" + hat"j"-2hat"k", and"hence find a vector perpendicular to both"  vec"a" + vec"b" and vec"a" - vec"b"`.

Answer 1

Here `vec"a" + vec"b" = 5hat"i" + hat"k" and vec"a" - vec"b" = -hat"i" -2hat"j" + 5hat"k"`.

Getting cos θ = 0

⇒ θ = `pi/2`

a vector perpendicular to both `veca + vecb  "and"  veca - vecb "is" ( veca + vecb ) xx (veca - vecb ) - 2hati - 26hatj - 10hatk`.