Question

Find the scalar product of the vectors \(\vec{a}=6\hat{i}-7\hat{j}+5\hat{k} \,and \,\vec{b}=6\hat{i}-7\hat{k}\)

(a) 1

(b) 8

(c) 6

(d) 3

This question was addressed to me during an interview.

My question is taken from Product of Two Vectors-1 topic in division Vector Algebra of Mathematics – Class 12

Answer 1

The correct answer is (a) 1

The explanation is: If \(\vec{a} \,and \,\vec{b}\) are two vectors, where \(a_1, a_2, a_3\) are the components of vector \(\vec{a} \,and \,b_1, b_2, b_3\) are the components of vector \(\vec{b}\), then the scalar product is given by

\(\vec{a}.\vec{b}=a_1 b_1+a_1 b_2+a_3 b_3\)

\((6\hat{i}-7\hat{j}+5\hat{k}).(6\hat{i}-7\hat{k})\)=6(6)-7(0)+5(-7)=36-35=1.