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If the vectors iikik-3i^+4i^-2k^,i^+2k^ and ipji^-pj^ are coplanar, then find the value of p. - Mathematics and Statistics

Sum

If the vectors `- 3hat"i" + 4hat"i" - 2hat"k" , hat"i" + 2hat"k"` and `hat"i" - "p"hat"j"` are coplanar, then find the value of p.

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Solution

Let `bar"a" = - 3hat"i" + 4hat"i" - 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),(1,0,0),(1,-"p",0)| = 0`

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

∴ - 6p + 8 + 2p = 0

∴ - 4p = - 8

∴ p = 2.

Concept: Scalar Triple Product of Vectors
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