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Question

The value of 'a' for which the vectors
A=2i-j-4k ,
B=i-5j+ak and
C=2i+3j+4k are linearly dependent is

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Solution

We now that the given vectors will be linearly dependent if

21415a234∣ ∣=0

solving the matrix
2(-5×4 - 3×a) - (-1)(1×4 - 2×a) + 4(1×3 - 2×(-5)) = 0
-40-6a+4-2a+12+40 = 0
a = 2
So for a = 2, the given vectors will be linearly dependent.

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