Question

Find vector \(\vec{c}\), if \(\vec{a}\)–\(\vec{b}\)+\(\vec{c}\)=6\(\hat{i}\)+8\(\hat{j}\) where \(\vec{a}\)=7\(\hat{i}\)+2\(\hat{j}\) and \(\vec{b}\)=4\(\hat{i}\)-5\(\hat{j}\).

(a) -3\(\hat{i}\)+\(\hat{j}\)

(b) 3\(\hat{i}\)+\(\hat{j}\)

(c) 3\(\hat{i}\)–\(\hat{j}\)

(d) -3\(\hat{i}\)–\(\hat{j}\)

The question was asked during an online interview.

This interesting question is from Addition of Vectors in division Vector Algebra of Mathematics – Class 12

Answer 1

The correct option is (b) 3\(\hat{i}\)+\(\hat{j}\)

The explanation: Given that, \(\vec{a}\)–\(\vec{b}\)+\(\vec{c}\)=6\(\hat{i}\)+8\(\hat{j}\) -(1)

It is also given that, \(\vec{a}\)=7\(\hat{i}\)+2\(\hat{j}\) and \(\vec{b}\)=4\(\hat{i}\)-5\(\hat{j}\)

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

\(\vec{a}\)–\(\vec{b}\)+\(\vec{c}\)=6\(\hat{i}\)+8\(\hat{j}\)

(7\(\hat{i}\)+2\(\hat{j}\))-(4\(\hat{i}\)-5\(\hat{j}\))+\(\vec{c}\)=6\(\hat{i}\)+8\(\hat{j}\)

∴\(\vec{c}\)=(6\(\hat{i}\)+8\(\hat{j}\))-(7\(\hat{i}\)+2\(\hat{j}\))+(4\(\hat{i}\)-5\(\hat{j}\))

=(6-7+4) \(\hat{i}\)+(8-2-5) \(\hat{j}\)

=3\(\hat{i}\)+\(\hat{j}\)