Question

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

Answer 1

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

To elaborate: To evaluate: \((\vec{a}+\vec{b}).(7\vec{a}-6\vec{b})\)

=\(\vec{a}.7\vec{a}-\vec{a}.6\vec{b}+\vec{b}.7\vec{a}-6\vec{b}.\vec{b}\)

=\(7|\vec{a}|^2+\vec{a}.\vec{b}-6|\vec{b}|^2\)