Question

Let v = `2hati + hatj - hatk` and w = `hati + 3hatk`. If u is a unit vector, then maximum value of scalar triple product [u v w] is ______.

Options

• – 1

• `sqrt(10) + sqrt(6)`

• `sqrt(59)`

• `sqrt(60)`

Answer 1

Let v = `2hati + hatj - hatk` and w = `hati + 3hatk`. If u is a unit vector, then maximum value of scalar triple product [u v w] is `underlinebb(sqrt(59))`.

Explanation:

∵ [u v w] = | u . (v × w)|

∵ v × w = `|(hati, hatj, hatk),(2, 1, -1),(1, 0, 3)|`

= `hati(3 - 0) - hatj(6 + 1) + hatk(0 - 1)`

= `3hati - 7hatj - hatk`

Now, `|u . (3hati - 7hatj - hatk)| = |u| sqrt(59) cos θ`

∴ Maximum [u v w] = `sqrt(59)`  ...[∴ |u| = 1, cos θ ≤ 1]