Vector Algebra Question 316
Question: If a, b, c are non-zero vectors such that $ \mathbf{a}.\mathbf{b}=\mathbf{a}.\mathbf{c}, $ then which statement is true
[RPET 2001]
Options:
A) b = c
B) $ \mathbf{a},\bot ,(\mathbf{b}-\mathbf{c}) $
C) $ \mathbf{b}=\mathbf{c} $ or $ \mathbf{a},\bot ,(\mathbf{b}-\mathbf{c}) $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- $ \mathbf{a}.\mathbf{b}=\mathbf{a}.\mathbf{c}\Rightarrow \mathbf{a}.\mathbf{b}-\mathbf{a}.\mathbf{c}=0\Rightarrow \mathbf{a}.(\mathbf{b}-\mathbf{c})=0 $
$ \Rightarrow $ Either $ \mathbf{b}-\mathbf{c}=\mathbf{0}or\mathbf{a}=\mathbf{0}\Rightarrow \mathbf{b}=\mathbf{c} $ or $ \mathbf{a}\bot (\mathbf{b}-\mathbf{c}). $
BETA
