Vector Algebra Question 342
Question: $ a,,b,,c $ are three vectors, such that $ a+b+c=0 $ , $ |a|,=1,,|b|,=2,,|c|,=3 $ , then $ a.b+b.c+c.a $ is equal to
[AIEEE 2003]
Options:
A) 0
B) ? 7
C) 7
D) 1
Show Answer
Answer:
Correct Answer: B
Solution:
- $ \mathbf{a}+\mathbf{b}+\mathbf{c}=0 $
Þ $ (\mathbf{a}+\mathbf{b}+\mathbf{c}),.,(\mathbf{a}+\mathbf{b}+\mathbf{c}) $ = 0
Þ $ |\mathbf{a}{{|}^{2}}+|\mathbf{b}{{|}^{2}}+|\mathbf{c}{{|}^{2}}+,2(\mathbf{a}\mathbf{.b}+\mathbf{b}\mathbf{.c}+\mathbf{c}\mathbf{.a})=0 $
Þ $ \mathbf{a}\mathbf{.b}+\mathbf{b}\mathbf{.c}+\mathbf{c}\mathbf{.a}=\frac{-1-4-9}{2}=-7. $
BETA
