Question

Find vector \(\vec{b}\), if \(\vec{a}+\vec{b}\)+\(\vec{c}\)=8\(\hat{i}\)+2\(\hat{j}\) where \(\vec{a}\)=\(\hat{i}\)-6\(\hat{j}\) and \(\vec{c}\)=3\(\hat{i}\)+7\(\hat{j}\).

(a) 4\(\hat{i}\)+4\(\hat{j}\)

(b) \(\hat{i}\)+4\(\hat{j}\)

(c) 4\(\hat{i}\)–\(\hat{j}\)

(d) 4\(\hat{i}\)+\(\hat{j}\)

This question was addressed to me in an interview for job.

I'm obligated to ask this question of Addition of Vectors topic in portion Vector Algebra of Mathematics – Class 12

Answer 1

Right choice is (d) 4\(\hat{i}\)+\(\hat{j}\)

To elaborate: Given that, \(\vec{a}+\vec{b}\)+\(\vec{c}\)=8\(\hat{i}\)+2\(\hat{j}\) -(1)

Given: \(\vec{a}\)=\(\hat{i}\)-6\(\hat{j}\) and \(\vec{c}\)=3\(\hat{i}\)+7\(\hat{j}\)

Substituting the values of \(\vec{a}\) and \(\vec{b}\) in equation (1), we get

\(\vec{a}+\vec{b}\)+\(\vec{c}\)=8\(\hat{i}\)+2\(\hat{j}\)

(\(\hat{i}\)-6\(\hat{j}\))+\(\vec{b}\)+(3\(\hat{i}\)+7\(\hat{j}\))=8\(\hat{i}\)+2\(\hat{j}\)

∴\(\vec{c}\)=(8\(\hat{i}\)+2\(\hat{j}\))-(\(\hat{i}\)-6\(\hat{j}\))-(3\(\hat{i}\)+7\(\hat{j}\))

=(8-1-3) \(\hat{i}\)+(2+6-7) \(\hat{j}\)

=4\(\hat{i}\)+\(\hat{j}\)