Question

The magnitude of the projection of the vector `2hati + 3hatj + hatk` on the vector perpendicular to the plane containing the vector `hati + hatj + hatk` and `hati + 2hatj + 3hatk`, is ______.

Options

• `3sqrt(6)`

• `sqrt(3)/2`

• `sqrt(6)`

• `sqrt(3/2)`

Answer 1

The magnitude of the projection of the vector `2hati + 3hatj + hatk` on the vector perpendicular to the plane containing the vector `hati + hatj + hatk` and `hati + 2hatj + 3hatk`, is `underlinebb(sqrt(3/2))`.

Explanation:

Plane ⊥ to `hati + hatj + hatk` and `hati + 2hatj + 3hatk`

`|(hati, hatj, hatk),(1, 1, 1),(1, 2, 3)| = hati(3 - 2) - hatj(3 - 1) + hatk(2 - 1)`

= `hati - 2hatj + hatk`

Projection of 2i + 3j + k on i – 2j + k is `((i - 2j + k)(2i + 3j + k))/sqrt(1 + 4 + 1) = sqrt(3/2)`