Question

Find the scalar product of the vectors \(\vec{a}=2\hat{i}+5\hat{j}\) and \(\vec{b}=6\hat{i}-7\hat{j}\).

(a) -32

(b) -23

(c) 32

(d) 23

This question was posed to me in an interview for internship.

My doubt stems from Product of Two Vectors-1 in section Vector Algebra of Mathematics – Class 12

Answer 1

Correct option is (b) -23

Best explanation: If \(\vec{a} \,and \,\vec{b}\) are two vectors, where a1, a2 are the components of vector \(\vec{a} \,and \,b_1, \,b_2\) are the components of vector \(\vec{b}\), then the scalar product is given by

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

∴\((2\hat{i}+5\hat{j}).(6\hat{i}-7\hat{j})\)=2(6)+5(-7)=12-35=-23.