Vector Algebra Question 290
Question: If vectors $ \mathbf{a},,b,,\mathbf{c} $ satisfy the condition $ |\mathbf{a}-\mathbf{c}|=|\mathbf{b}-\mathbf{c}| $ , then $ (\mathbf{b}-\mathbf{a}),.,( \mathbf{c}-\frac{\mathbf{a}+\mathbf{b}}{\mathbf{2}} ) $ is equal to
[AMU 1999]
Options:
A) 0
B) ?1
C) 1
D) 2
Show Answer
Answer:
Correct Answer: A
Solution:
- $ (\mathbf{b}-\mathbf{a}),.,( \mathbf{c}-\frac{\mathbf{a}+\mathbf{b}}{2} )=\mathbf{b},.,\mathbf{c}-\mathbf{b},.,( \frac{\mathbf{a}+\mathbf{b}}{2} ),-\mathbf{a},.,\mathbf{c}+\frac{\mathbf{a}}{2}(\mathbf{a}+\mathbf{b}) $ and $ |\mathbf{a}-\mathbf{c}|,=,|\mathbf{b}-\mathbf{c}| $
$ \Rightarrow $ $ ,|\mathbf{a}-\mathbf{c}{{|}^{2}},=,|\mathbf{b}-\mathbf{c}{{|}^{2}} $ \ $ \mathbf{a}+\mathbf{b}=2\mathbf{c} $ Therefore, $ (\mathbf{b}-\mathbf{a}).,( \mathbf{c}-\frac{\mathbf{a}+\mathbf{b}}{2} )=0. $
BETA
