Vector Algebra Question 349
Question: If a and b are two non-collinear vectors and $ x,\mathbf{a}+y,\mathbf{b}=0 $
[RPET 2001]
Options:
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
Show Answer
Answer:
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.
BETA
