Vector Algebra Question 324
Question: If a, b, c are mutually perpendicular unit vectors, then $ |\mathbf{a}+\mathbf{b}+\mathbf{c}|= $
[Karnataka CET 2002, 05; J & K 2005]
Options:
A) $ \sqrt{3} $
B) 3
C) 1
D) 0
Show Answer
Answer:
Correct Answer: A
Solution:
- Three mutually perpendicular unit vectors $ =\mathbf{a} $ , $ \mathbf{b} $ and $ \mathbf{c} $ . Therefore $ |\mathbf{a}|,=,|\mathbf{b}|,=,|\mathbf{c}|,=1 $ and $ \mathbf{a}.\mathbf{b}=\mathbf{b}.\mathbf{c}=\mathbf{c}.\mathbf{a}=0 $ . We know that $ |\mathbf{a}+\mathbf{b}+\mathbf{c}{{|}^{2}}=(\mathbf{a}+\mathbf{b}+\mathbf{c}),.,(\mathbf{a}+\mathbf{b}+\mathbf{c})=|\mathbf{a}{{|}^{2}}+|\mathbf{b}{{|}^{2}} $ $ +|\mathbf{c}{{|}^{2}}+2(\mathbf{a},.,\mathbf{b}+\mathbf{b},.,\mathbf{c},+\mathbf{c},.,\mathbf{a})=1+1+1+0=3 $ or $ |\mathbf{a}+\mathbf{b}+\mathbf{c}|,=\sqrt{3}. $
BETA
