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