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
Correct Answer: D
Solution :
[d] \[(\vec{a}\times \vec{b})\times \vec{c}=\vec{a}\times (\vec{b}\times \vec{c}),\vec{a}.\vec{b}\ne 0,\vec{b}.\vec{c}\ne 0\] \[\Rightarrow (\vec{a}.\vec{c}).\vec{b}-(\vec{b}.\vec{c})\vec{a}=(\vec{a}.\vec{c}).\vec{b}-(\vec{a}.\vec{b}).\vec{c}\] \[\Rightarrow (\vec{a}.\vec{b}).\vec{c}=(\vec{b}.\vec{c})\vec{a}\Rightarrow \vec{a}\parallel \vec{c}.\]You need to login to perform this action.
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