# 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

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")

#### 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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