Vector Algebra Question 54
Question: If $ (\vec{a}\times \vec{b})\times \vec{c}=\vec{a}\times (\vec{b}\times \vec{c}) $ where $ \vec{a},\vec{b} $ and $ \vec{c} $ are any three vectors such that $ \vec{a}.\vec{b}\ne 0,\vec{b}.\vec{c}\ne 0 $ then $ \vec{a} $ and $ \vec{c} $ are
Options:
A) Inclined at an angle of $ \frac{\pi }{3} $ between them
B) Inclined at an angle of $ \frac{\pi }{6} $ between them
C) Perpendicular
D) Parallel
Show Answer
Answer:
Correct Answer: D
Solution:
- [d] $ (\vec{a}\times \vec{b})\times \vec{c}=\vec{a}\times (\vec{b}\times \vec{c}),\vec{a}.\vec{b}\ne 0,\vec{b}.\vec{c}\ne 0 $
$ \Rightarrow (\vec{a}.\vec{c}).\vec{b}-(\vec{b}.\vec{c})\vec{a}=(\vec{a}.\vec{c}).\vec{b}-(\vec{a}.\vec{b}).\vec{c} $
$ \Rightarrow (\vec{a}.\vec{b}).\vec{c}=(\vec{b}.\vec{c})\vec{a}\Rightarrow \vec{a}\parallel \vec{c}. $
BETA
