Question

Find the value of λ such that the vectors `vec"a" = 2hat"i" + lambdahat"j" + hat"k"` and `vec"b" = hat"i" + 2hat"j" + 3hat"k"` are orthogonal ______.

Options

• 0

• 1

• `3/2`

• `- 5/2`

Answer 1

Find the value of λ such that the vectors `vec"a" = 2hat"i" + lambdahat"j" + hat"k"` and `vec"b" = hat"i" + 2hat"j" + 3hat"k"` are orthogonal `- 5/2`.

Explanation:

Given that `vec"a" = 2hat"i" + lambdahat"j" + hat"k"` 

And `vec"b" = hat"i" + 2hat"j" + 3hat"k"`

Since `vec"a"` and `vec"b"` are orthogonal

∴ `vec"a" * vec"b"` = 0

⇒ `(2hat"i" + lambdahat"j" + hat"k") * (hat"i" + 2hat"j" + 3hat"k")` = 0

⇒ 2 + 2λ + 3 = 0

⇒ 5 + 2λ = 0

⇒ λ = `(-5)/2`