Question

Find the sum of the vectors \(\vec{a}\)=6\(\hat{i}\)-3\(\hat{j}\) and \(\vec{b}\)=5\(\hat{i}\)+4\(\hat{j}\).

(a) 11\(\hat{i}\)+\(\hat{j}\)

(b) 11\(\hat{i}\)–\(\hat{j}\)

(c) -11\(\hat{i}\)+\(\hat{j}\)

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

I had been asked this question in semester exam.

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

Answer 1

Correct answer is (a) 11\(\hat{i}\)+\(\hat{j}\)

The explanation: Given that, \(\vec{a}\)=6\(\hat{i}\)-3\(\hat{j}\) and \(\vec{b}\)=5\(\hat{i}\)+4\(\hat{j}\)

The sum of the vectors is given by \(\vec{a}+\vec{b}\).

∴\(\vec{a}+\vec{b}\)=(6\(\hat{i}\)-3\(\hat{i}\))+(5\(\hat{i}\)+4\(\hat{j}\))

=(6+5) \(\hat{i}\)+(-3+4)\(\hat{j}\)

=11\(\hat{i}\)+\(\hat{j}\)