A) \[\vec{b}+\vec{c}\]
B) \[\vec{b}-2\vec{c}\]
C) \[\vec{b}+2\vec{c}\]
D) \[\vec{b}-\vec{c}\]
Correct Answer: D
Solution :
Now, \[(\vec{a}-\vec{d})\times (\vec{b}-\vec{c})=\vec{a}\times \vec{b}-\vec{a}\times \vec{c}-\vec{d}\times \vec{b}\] \[+\vec{d}\times \vec{c}\] \[=\vec{c}\times \vec{d}-\vec{b}\times \vec{d}-\vec{d}\times \vec{b}+\vec{d}\times \vec{c}\] \[[\because \,\vec{a}\times \overset{\scriptscriptstyle\rightharpoonup}{b}=\vec{c}\times \vec{d},\vec{a}\times \vec{c}=\vec{b}\times \vec{d}\,given]\] = \[\vec{0}\] \[\Rightarrow \] \[(\vec{a}-\vec{d})||(\vec{b}-\vec{c})\]
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