If \vec{a} \,and \,\vec{b} are two non-zero vectors then (\vec{a}-\vec{b})×(\vec{a}+\vec{b})=_________

Category: QuestionsIf \vec{a} \,and \,\vec{b} are two non-zero vectors then (\vec{a}-\vec{b})×(\vec{a}+\vec{b})=_________
Editor">Editor Staff asked 11 months ago

If \vec{a} \,and \,\vec{b} are two non-zero vectors then (\vec{a}-\vec{b})×(\vec{a}+\vec{b})=_________
(a) 2(\vec{a}×\vec{b})
(b) (\vec{a}×\vec{b})
(c) –4(\vec{a}×\vec{b})
(d) 3(\vec{a}×\vec{b})
This question was posed to me during an online interview.
My doubt stems from Product of Two Vectors-2 in portion Vector Algebra of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

The correct option is (a) 2(\vec{a}×\vec{b})
To explain: Consider (\vec{a}-\vec{b})×(\vec{a}+\vec{b})
We know that, \vec{a}×\vec{a}=0,\vec{b}×\vec{b}=0 \,and \,\vec{a}×\vec{b}=-\vec{b}×\vec{a}
∴ \vec{a}×\vec{a}-\vec{b}×\vec{a}+\vec{a}×\vec{b}-\vec{b}×\vec{b}=0+2(\vec{a}×\vec{b})+0
Hence, (\vec{a}-\vec{b})×(\vec{a}+\vec{b})=2(\vec{a}×\vec{b})