Question

The value of m for which the points with position vectors `-hati -hatj + 2hatk, 2hati + mhatj + 5hatk and 3hati + 11hatj + 6hatk` are collinear, is ______.

Options

• 8

• −8

• 2

• `5/2`

Answer 1

The value of m for which the points with position vectors `-hati -hatj + 2hatk, 2hati + mhatj + 5hatk and 3hati + 11hatj + 6hatk` are collinear, is 8.

Explanation:

Let points be A(−1, −1, 2), B(2, m, 5), C(3, 11, 6).

For collinearity,

`vec(AB) = lambda vec(AC)`

`vec(AB) = (3, m + 1, 3)`,

`vec(AC) = (4, 12, 4)`

Comparing ratios:

`3/4 = (m + 1)/12 = 3/4`

Thus, m + 1 = 9

∴ m = 8