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If the vectors iqjk2i^-qj^+3k^ and ijk4i^-5j^+6k^ are collinear, find q. - Mathematics and Statistics

Sum

If the vectors `2hat"i" - "q"hat"j" + 3hat"k"` and `4hat"i" - 5hat"j" + 6hat"k"` are collinear, find q.

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Solution

The vectors `2hat"i" - "q"hat"j" + 3hat"k"` and `4hat"i" - 5hat"j" + 6hat"k"` are collinear

∴ the coefficients of `hat"i",hat"j", hat"k"` are proportional

`∴ 2/4 = (-"q")/-5 = 3/6`

`∴ "q"/5 = 1/2`

`∴ "q" = 5/2`

Concept: Representation of Vector
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