Question

Let `bara = hati + 2hatj + hatk, barb = hati - hatj + hatk and barc = hati + hatj - hatk`.

A vector in the plane of `bara and barb` whose projection on `barc` is `1/sqrt3`, is

Options

• `4hati - hatj + 4hatk`

• `3hati + hatj - 3hatk`

• `2hati + hatj - 2hatk`

• `4hati + hatj - 4hatk`

Answer 1

`bb(4hati - hatj + 4hatk)`

Explanation:

A vector in the plane of `bara and hatb` is

`baru = bara + lambdabarb = (1 + lambda)hati + (2 - lambda)hatj + (1 + lambda)hatk`

Projection of `baru` on `barc = 1/sqrt3`

= `(baru.barc)/(|barc|) = 1/sqrt3`

= `baru.barc = 1 = |1 + lambda + 2 - lambda - 1 - lambda| = 1`

= |2 − λ| = 1 = λ = 1 or 3

= `batu = 2hati + hatj + 2hatk` or `4hati - hatj + 4hatk`