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Question
If the vectors `- 3hat"i" + 4hat"j" - 2hat"k" , hat"i" + 2hat"k"` and `hat"i" - "p"hat"j"` are coplanar, then find the value of p.
Solution
Let `bar"a" = - 3hat"i" + 4hat"j" - 2hat"k" , bar"b" = hat"i" + 2hat"k" , bar"c" = hat"i" - "p"hat"j"`
Then `bar"a", bar"b", bar"c"` are coplanar.
∴ `[bar"a" bar"b" bar"c"] = 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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