Question

The projection of `hati + 2hatj − 3hatk` on 2`hati − hatj + hatk` is ______.

Options

• `sqrt3/sqrt2`

• `(−sqrt3)/sqrt2`

• `(−3)/2`

• `(−sqrt3)/2`

Answer 1

The projection of `hati + 2hatj − 3hatk` on 2`hati − hatj + hatk` is `underlinebb((−sqrt3)/sqrt2`.

Explanation:

The projection of vector `hata` on `hatb` is calculated using the formula `(veca.vecb)/|vecb|` here, the dot product `veca.vecb` = (1) (2) + (2) (−1) + (−3)(1) = −3 and the magnitude `|hatb|`.

= `sqrt((2^2 + (−1)^2 + 1^2)`

= `sqrt6`

Thus, the projection is `(−3)/sqrt6`, which simplifies to `(− sqrt3)/sqrt2`.