Question

If `hati - 2hatj + hatk`, `2hati + phatj + 3hatk` and `5hati - 9hatj + 4hatk` are coplanar, then the value of p is equal to ______

Options

• 4

• -4

• 5

• -5

Answer 1

If `hati - 2hatj + hatk`, `2hati + phatj + 3hatk` and `5hati - 9hatj + 4hatk` are coplanar, then the value of p is equal to -5.

Explanation:

Since the vectors are coplanar,

`[overlinea  overlineb  overlinec] = 0`

⇒ `|(1, -2, 1), (2, p, 3), (5, -9, 4)| = 0`

⇒ 1(4p + 27) + 2(8 - 15) + 1(-18 - 5p) = 0

⇒ p = -5