Maharashtra State BoardHSC Arts 12th Board Exam
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If the vectors 2i^-qj^+3k^ and 4i^-5j^+6k^ are collinear then find the value of q - Mathematics and Statistics

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Sum

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

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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`

Concept: Vector Joining Two Points
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