A) \[x=0\], but y is not necessarily zero
B) \[y=0\], but x is not necessarily zero
C) \[x=0\], \[y=0\]
D) None of these
Correct Answer: C
Solution :
If \[\mathbf{a},\,\,\mathbf{b}\] are two non-zero, non-collinear vectors and x, y are two scalars such that \[x\mathbf{a}+y\mathbf{b}=0,\] then \[x=0,\,\,y=0\]. Because otherwise one will be a scalar multiple of the other and hence collinear which is a contradiction.
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