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
Open in App
Solution
We now that the given vectors will be linearly dependent if
⎛⎜⎝2−141−5a234∣∣
∣∣=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.