Question

Find the value λ for which the vectors `vec"a"` and  `vec"b"` are perpendicular, where `vec"a" = 2hat"i" + lambdahat"j" + hat"k"` and `vec"b" = hat"i" - 2hat"j" + 3hat"k"`

Answer 1

When `vec"a"` and `vec"b"` are ⊥^r then `vec"a"*vec"b"` = 0

`vec"a"` ⊥^r  `vec"b"` ⇒ `vec"a" * vec"b"` = 0

(2)(1) + (λ)(– 2) + (1)(3) = 0

⇒ λ = `5/2`