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 
Interview Questions and Answers, Database Interview Questions and Answers for Freshers and Experience

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})
 
=(\vec{a}-\vec{b})×\vec{a}+(\vec{a}+\vec{b})×\vec{b}
 
=\vec{a}×\vec{a}-\vec{b}×\vec{a}+\vec{a}×\vec{b}-\vec{b}×\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})