Question

The value of α if the angle between `overset->p = 2alpha^2hati - 3alphahatj + hatk and overset->q = hati + hatj + alphahatk`  is obtuse is ______.

Options

• R − [0, 1]

• (0, 1)

• [0, ∞)

• [1, ∞)

Answer 1

The value of α if the angle between `overset->p = 2alpha^2hati - 3alphahatj + hatk and overset->q = hati + hatj + alphahatk`  is obtuse is (0, 1).

Explanation:

For obtuse angle, `cosθ < 0 => overset->p*overset->q < 0`

2α² − 3α + α < 0

⇒ 2α² − 2α < 0

⇒ α ∈ (0, 1)