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Question

If the vectors a+λb+3c,2a+3b4c and a3b+5c are coplanar, then the value of λ is

A
2
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B
-1
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C
1
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D
-2
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Solution

The correct option is D -2
Since, the given three vectors are coplanar, therefore one of them should be expressible as a linear combination of the remaining two ie, there should exist two scalars x and y such that
a+λb+3c=x(2a+3b4c)+y(a3b+5c)
2x+y=1;3x3y=λ ; and 3 =-4x +5y
Solving first and third equations, we get x=13,y=13.
Since, the vectors are coplanar, therefore these values of x and y also satisfy the third equation
λ=2

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