Question

Find the magnitude of \(\vec{a}+\vec{b}\), if \(\vec{a}\)=4\(\hat{i}\)+9\(\hat{j}\) and \(\vec{b}\)=6\(\hat{i}\).

(a) \(\sqrt{181}\)

(b) \(\sqrt{81}\)

(c) \(\sqrt{11}\)

(d) \(\sqrt{60}\)

This question was addressed to me in final exam.

The query is from Addition of Vectors topic in section Vector Algebra of Mathematics – Class 12

Answer 1

Correct answer is (a) \(\sqrt{181}\)

To explain I would say: Given that, \(\vec{a}\)=4\(\hat{i}\)+9\(\hat{j}\) and \(\vec{b}\)=6\(\hat{i}\)

∴\(\vec{a}+\vec{b}\)=(4+6) \(\hat{i}\)+9\(\hat{j}\)

=10\(\hat{i}\)+9\(\hat{j}\)

|\(\vec{a}+\vec{b}\)|=\(\sqrt{10^2+9^2}=\sqrt{100+81}=\sqrt{181}\)