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

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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}