Question

Evaluate the product \((2\vec{a}+5\vec{b}).(4\vec{a}-5\vec{b})\).

(a) \(|\vec{a}|^2+2\vec{a}.\vec{b}-15|\vec{b}|^2\)

(b) \(8|\vec{a}|^2+2\vec{a}.\vec{b}-15|\vec{b}|^2\)

(c) \(8|\vec{a}|^2-4\vec{a}.\vec{b}-15|\vec{b}|^2\)

(d) \(|\vec{a}|^2+\vec{a}.\vec{b}-5|\vec{b}|^2\)

The question was asked by my school principal while I was bunking the class.

The query is from Product of Two Vectors-2 topic in chapter Vector Algebra of Mathematics – Class 12

Answer 1

Correct answer is (b) \(8|\vec{a}|^2+2\vec{a}.\vec{b}-15|\vec{b}|^2\)

The best I can explain: To evaluate: \((2\vec{a}+5\vec{b}).(4\vec{a}-5\vec{b})\)

=\(2\vec{a}.4\vec{a}-2\vec{a}.5\vec{b}+3\vec{b}.4\vec{a}-3\vec{b}.5\vec{b}\)

=\(8|\vec{a}|^2+2\vec{a}.\vec{b}-15|\vec{b}|^2\)