If the points P(a + 2b + c), Q(2a + 3b), R (b + tc) are collinear, where a, b and c are three non-coplanar vectors, the value of t is

Options

A. `-2`
B. `-1//2`
C. `1//2`
D. 2

Answer

D

Explanation

It is given that the points
P(a + 2b + c), Q (2a + 3b) and R(b + t c) are collinear.
`therefore PQ = lambda QR" for some scalar "lambda`
`implies a+b-c=lambda(-2a-2b+tc)`
`implies (2lambda+1)a+(1+2lambda)b-(t lambda+1)c=0`
`implies 2lambda+1=0, 2lambda+1=0, tlambda+1=0` [`because` a, b and c are non-coplanar]
implies t = 2