Find the product (\vec{a}+\vec{b}).(7\vec{a}-6\vec{b}).

Category: QuestionsFind the product (\vec{a}+\vec{b}).(7\vec{a}-6\vec{b}).
Editor">Editor Staff asked 11 months ago

Find the product (\vec{a}+\vec{b}).(7\vec{a}-6\vec{b}).
 
(a) 2|\vec{a}|^2+6\vec{a}.\vec{b}-3|\vec{b}|^2
 
(b) 8|\vec{a}|^2+5\vec{a}.\vec{b}-5|\vec{b}|^2
 
(c) 2|\vec{a}|^2+6\vec{a}.\vec{b}-8|\vec{b}|^2
 
(d) 7|\vec{a}|^2+\vec{a}.\vec{b}-6|\vec{b}|^2
 
The question was posed to me during an online exam.
 
My enquiry is from Product of Two Vectors-2 topic in chapter 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

Correct option is (d) 7|\vec{a}|^2+\vec{a}.\vec{b}-6|\vec{b}|^2
 
To elaborate: To evaluate: (\vec{a}+\vec{b}).(7\vec{a}-6\vec{b})
 
=\vec{a}.7\vec{a}-\vec{a}.6\vec{b}+\vec{b}.7\vec{a}-6\vec{b}.\vec{b}
 
=7|\vec{a}|^2+\vec{a}.\vec{b}-6|\vec{b}|^2