Question

If the vectors `hat"i" + hat"j" + hat"k"`, `hat"i" - hat"j" + hat"k"` and `2hat"i" + 3hat"j" + "m"hat"k"` are coplanar, then m = ____________.

Options

• 3

• 2

• −3

• −2

Answer 1

If the vectors `hat"i" + hat"j" + hat"k"`, `hat"i" - hat"j" + hat"k"` and `2hat"i" + 3hat"j" + "m"hat"k"` are coplanar, then m = 2.

Explanation:

Given vector  `hat"i" + hat"j" + hat"k"`, `hat"i" - hat"j" + hat"k"` and `2hat"i" + 3hat"j" + "m"hat"k"` are coplanar

∴ `|(1, 1, 1), (1, -1, 1), (2, 3, "m")|` = 0

1(−m − 3) − 1(m − 2) + 1(3 + 2) = 0

−m − 3 − m + 2 + 5 = 0

2m = 4

m = 2