Question

Three coplanar vectors in arbitrary units are given by \( \vec{A}=4 \hat{i}+2 \hat{j}-3 \hat{k}, \quad \vec{B}=\hat{i}+\hat{j}+3 \hat{k} \quad \) and \( \vec{C}=4 \hat{i}+5 \hat{j}+3 \hat{k} \), the resultant is a) \( 8 \hat{i}+3 \hat{j}+3 \hat{k} \) b) \( 5 \hat{i}+3 \hat{j}-3 \hat{k} \) c) \( 9 \hat{i}+8 \hat{j}+12 \hat{k} \) d) \( 9 \hat{i}+8 \hat{j}+3 \hat{k} \)

Answer 1

Correct option is (d) \(9\hat i + 8\hat j + 3\hat k\)

Three coplanar vectors are given by \(\vec A = 4\hat i + 2\hat j - 3\hat k, \vec B = \hat i + \hat j + 3\hat k\) and \(\vec C = 4\hat i + 5\hat j + 3 \hat k\)

The resultant \(\vec R\) of the three vectors is,

\(\vec R = \vec A + \vec B + \vec C\)

\(\vec R = 4\hat i + 2 \hat j - 3 \hat k + \hat i + \hat j + 3 \hat k + 4 \hat i + 5 \hat j + 3 \hat k\)

\(\vec R = 9\hat i + 8\hat j + 3\hat k\)