1.

A, B and C are three non-zero vectors, no two of them are parallel. If A + B is collinear to C and B + C is collinear to A, then A + B + C is equal to

Answer»

A
B
C
0

Solution :Since, A + B is collinear to C and B + C is collinear to A.
`therefore A + B = lambda C`
and `B + C = MU A`
where, `lambda` and `mu` are SCALARS.
`implies A+B+C=(lambda+1)C`
and `A+B+C=(mu+1)A`
`implies (lambda+1)C=(mu+1)A`
If `lambda ne-1`, then
`C=(mu+1)/(lambda+1)A`
implies C and A are collinear.
This is a contradiction to the given CONDITION.
`therefore lambda = - 1`
`therefore A + B + C = 0`


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