Question

Find the value of λ for which the vectors `vec"a" = 3hat"i" + 2hat"j" + 9hat"k"` and `hat"b" = hat"i" + lambdahat"j" + 3hat"k"` are parallel

Answer 1

Given that the vectors `vec"a" = 3hat"i" + 2hat"j" + 9hat"k"` and `hat"b" = hat"i" + lambdahat"j" + 3hat"k"` are parallel.

∴ `vec"a"  = "m"vec"b"`

The condition forthe two vectors `vec"a"` and `vec"b"` to be parallel is `vec"a" = lambda vec"b"`

`3hat"i" + 2hat"j" + 9hat"k" = "m"(hat"i" + lambdahat"j" + 3hat"k")`

`3hat"i" + 2hat"j" + 9hat"k" = "m"hat"i" + "m"lambdahat"j" + 3"m"hat"k"`

`(3 - "m")hat"i" + (2 - lambda"m")hat"j" + (9 - 3"m")hat"k"` = 0

∴ `3 - "m" = 0, 2 - lambda"m" = 0, 9 - 3"m" = 0`

m = 3, 2 = `lambda"m"`

2 = `lambda xx 3`

⇒ `lambda = 2/3`

∴ Required value of `lambda` is `2/3`.