Question

If the vectors `- 3hati + 4hatj - 2hatk , hati + 2hatk` and `hati - phatj` are coplanar, then find the value of p.

Answer 1

Let `bara = - 3hati + 4hatj - 2hatk, barb = hati + 2hatk, barc = hati - phatj`

Then `bara, barb, barc` are coplanar.

∴ `[bara  barb  barc] = 0`

∴ `|(-3,4,-2),(1,0,2),(1,-p,0)| = 0`

∴ −3(0 + 2p) − 4(0 − 2) − 2(− p − 0) = 0

∴ −6p + 8 + 2p = 0

∴ −4p = −8

∴ p = 2