Question

If \(\vec{a}\)=\(\hat{i}\)+4\(\hat{j}\) and \(\vec{b}\)=3\(\hat{i}\)-3\(\hat{j}\). Find the magnitude of \(\vec{a}+\vec{b}\).

(a) \(\sqrt{6}\)

(b) \(\sqrt{11}\)

(c) \(\sqrt{5}\)

(d) \(\sqrt{17}\)

I had been asked this question in homework.

My question is from Addition of Vectors topic in portion Vector Algebra of Mathematics – Class 12

Answer 1

The correct choice is (d) \(\sqrt{17}\)

Explanation: Given that, \(\vec{a}\)=\(\hat{i}\)+4\(\hat{j}\) and \(\vec{b}\)=3\(\hat{i}\)-3\(\hat{j}\)

∴\(\vec{a}+\vec{b}\)=(1+3) \(\hat{i}\)+(4-3) \(\hat{j}\)

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

|\(\vec{a}+\vec{b}\)|=\(\sqrt{4^2+1^2}=\sqrt{16+1}=\sqrt{17}\)