Question

If \(\vec{a}\)=3\(\hat{i}\)+2\(\hat{j}\)+2\(\hat{k}\), \(\vec{b}\)=2\(\hat{i}\)-8\(\hat{j}\)+\(\hat{k}\), find \(\vec{a}+\vec{b}\).

(a) 5\(\hat{i}\)+\(\hat{j}\)+3\(\hat{k}\)

(b) 5\(\hat{i}\)-6\(\hat{j}\)+3\(\hat{k}\)

(c) 5\(\hat{i}\)-6\(\hat{j}\)-3\(\hat{k}\)

(d) 5\(\hat{i}\)+6\(\hat{j}\)+3\(\hat{k}\)

The question was posed to me in a national level competition.

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

Answer 1

Right choice is (b) 5\(\hat{i}\)-6\(\hat{j}\)+3\(\hat{k}\)

The best I can explain: It is given that, \(\vec{a}\)=3\(\hat{i}\)+2\(\hat{j}\)+2\(\hat{k}\), \(\vec{b}\)=2\(\hat{i}\)-8\(\hat{j}\)+\(\hat{k}\)

To find: \(\vec{a}+\vec{b}\)

∴\(\vec{a}+\vec{b}\)=(3\(\hat{i}\)+2\(\hat{j}\)+2\(\hat{k}\))+(2\(\hat{i}\)-8\(\hat{j}\)+\(\hat{k}\))

=(3+2) \(\hat{i}\)+(2-8) \(\hat{j}\)+(2+1)\(\hat{k}\)

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