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Question
If the vectors `2hat"i" - "q"hat"j" + 3hat"k"` and `4hat"i" - 5hat"j" + 6hat"k"` are collinear then find the value of q
Solution
Let `bar("a") = 2hat"i" - "q"hat"j" + 3hat"k"` and `bar("b") = 4hat"i" - 5hat"j" + 6hat"k"`
Since `bar("a")` and `bar("b")` are collinear, there exists a scalar t such that `bar("b") = "t"bar("a")`
∴ `4hat"i" - 5hat"j"+ 6hat"k" = "t"(2hat"i" - "q"hat"j" + 3hat"k")`
= `2"t"hat"i" - "qt"hat"j" + 3"t"hat"k"`
∴ By equality of vectors, we get
∴ 4 = 2t, −5 = − qt, 6 = 3t
∴ 4 = 2t and − 5 = − qt
∴ t = 2 and − 5 = − q(2)
∴ – 5 = – 2q
∴ q = `5/2`
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