Question

Find λ, when the projection of `vec"a" = lambdahat"i" + hat"j" + 4hat"k"` on `vec"b" = 2hat"i" + 6hat"j" + 3hat"k"` is 4 units

Answer 1

The given vectors are `vec"a" = lambdahat"i" + hat"j" + 4hat"k"`, `vec"b" = 2hat"i" + 6hat"j" + 3hat"k"`

Also given that projection of a⃗  and b⃗  is 4 units.

`(vec"a" * vec"b")/|vec"b"|` = 4

`((lambdahat"i" + hat"j" + 4hat"k")*(2hat"i" + 6hat"j" + 3hat"k"))/|2hat"i" + 6hat"j" + 3hat"k"|` = 4

`((lambda)(2) + (1)(6) + (4)(3))/sqrt(2^2 + 6^2 + 3^2)` = 4

`(2lambda + 6 + 12)/sqrt(4 + 36 + 9)` = 4

`(2lambda + 18)/sqrt(49)` = 4

2λ + 18 = 4 × 7

2λ = 28 – 18

2λ = 10

⇒ λ = 5