Question

If \(\vec{a}\)=9\(\hat{i}\)-2\(\hat{j}\)+7\(\hat{k}\), \(\vec{b}\)=5\(\hat{i}\)+\(\hat{j}\)-3\(\hat{k}\), find \(\vec{a}+\vec{b}\).

(a) \(\hat{i}\)–\(\hat{j}\)+4\(\hat{k}\)

(b) 14\(\hat{i}\)–\(\hat{j}\)+4\(\hat{k}\)

(c) 14\(\hat{i}\)-3\(\hat{j}\)+4\(\hat{k}\)

(d) 14\(\hat{i}\)–\(\hat{j}\)+9\(\hat{k}\)

I had been asked this question in final exam.

This intriguing question comes from Addition of Vectors in division Vector Algebra of Mathematics – Class 12

Answer 1

The correct choice is (b) 14\(\hat{i}\)–\(\hat{j}\)+4\(\hat{k}\)

The best I can explain: Given that, \(\vec{a}\)=9\(\hat{i}\)-2\(\hat{j}\)+7\(\hat{k}\), \(\vec{b}\)=5\(\hat{i}\)+\(\hat{j}\)-3\(\hat{k}\)

We have to find \(\vec{a}+\vec{b}\)

∴\(\vec{a}+\vec{b}\)=(9\(\hat{i}\)-2\(\hat{j}\)+7\(\hat{k}\))+(5\(\hat{i}\)+\(\hat{j}\)-3\(\hat{k}\))

=(9+5) \(\hat{i}\)+(-2+1) \(\hat{j}\)+(7-3)\(\hat{k}\)

=14\(\hat{i}\)–\(\hat{j}\)+4\(\hat{k}\)