Question

Find the value of \(\vec{a}+\vec{b}\)+\(\vec{c}\), if \(\vec{a}\)=4\(\hat{i}\)-4\(\hat{j}\), \(\vec{b}\)=-3\(\hat{i}\)+2k, \(\vec{c}\)=7\(\hat{j}\)-8\(\hat{k}\).

(a) \(\hat{i}\)-3\(\hat{j}\)

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

(c) \(\hat{i}\)+\(\hat{j}\)+6\(\hat{k}\)

(d) \(\hat{i}\)+6\(\hat{k}\)

I had been asked this question during an online exam.

I'm obligated to ask this question of Addition of Vectors in portion Vector Algebra of Mathematics – Class 12

Answer 1

The correct option is (b) \(\hat{i}\)+3\(\hat{j}\)-6\(\hat{k}\)

For explanation: Given that, \(\vec{a}\)=4\(\hat{i}\)-4\(\hat{j}\), \(\vec{b}\)=-3\(\hat{i}\)+2k, \(\vec{c}\)=7\(\hat{j}\)-8\(\hat{k}\)

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

∴\(\vec{a}+\vec{b}\)+\(\vec{c}\)=(4\(\hat{i}\)-4\(\hat{j}\)) +(-3\(\hat{i}\)+2k) +(7\(\hat{j}\)-8\(\hat{k}\))

=(4-3) \(\hat{i}\)+(-4+7) \(\hat{j}\)+(2-8)\(\hat{k}\)

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