Maharashtra State BoardHSC Arts 12th Board Exam
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The non zero vectors a¯ and b¯ are not collinear find the value of λ and μ: if a¯+3b¯=2λa¯-μb¯ - Mathematics and Statistics

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Sum

The non zero vectors `bar("a")` and `bar("b")` are not collinear find the value of `lambda` and `mu`: if `bar("a") + 3bar("b") = 2lambdabar("a") - mubar("b")`

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Solution

`bar("a") + 3bar("b") = 2lambdabar("a") - mubar("b")`

∴ `(1 - 2lambda)bar("a") = (-3 - mu)bar("b")`

∴  `(1 - 2llambda)bar("a") + (3 + mu)bar("b")` = 0

If two vectors `bar("a")` and `bar("b")` are not collinear and `"m"bar("a") + "n"bar("b")` = 0, then m = 0, n = 0

∴  `1 - 2lambda` = 0 and `3 + mu` = 0

∴ `lambda = 1/2` and `mu` = – 3

Concept: Vector Joining Two Points
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