Question

Find the sum of the vectors \(\vec{a}\)=8\(\hat{i}\)+5\(\hat{j}\) and \(\vec{b}\)=-2\(\hat{i}\)+6\(\hat{j}\)

(a) 6\(\hat{i}\)+\(\hat{j}\)

(b) 6\(\hat{i}\)+11\(\hat{j}\)

(c) 6\(\hat{i}\)-11\(\hat{j}\)

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

The question was asked by my school teacher while I was bunking the class.

The above asked question is from Addition of Vectors topic in portion Vector Algebra of Mathematics – Class 12

Answer 1

The correct option is (b) 6\(\hat{i}\)+11\(\hat{j}\)

Explanation: Given that, \(\vec{a}\)=8\(\hat{i}\)+5\(\hat{j}\) and \(\vec{b}\)=-2\(\hat{i}\)+6\(\hat{j}\)

∴The sum of the vectors will be

\(\vec{a}+\vec{b}\)=(8\(\hat{i}\)+5\(\hat{j}\))+(-2\(\hat{i}\)+6\(\hat{j}\))

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

=6\(\hat{i}\)+11\(\hat{j}\)