If \(\vec{a}=\hat{\imath}+2\hat{\jmath}+3\hat{k}\) and \(\vec{b}=-\hat{\imath}+2\hat{k}\), then \(|2\vec{a}+\vec{b}|\) is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 9
Using scalar multiplication and addition component by component:
\(2\vec{a} = 2\hat{\imath}+4\hat{\jmath}+6\hat{k}\)
\(2\vec{a}+\vec{b} = (2-1)\hat{\imath}+4\hat{\jmath}+(6+2)\hat{k} = \hat{\imath}+4\hat{\jmath}+8\hat{k}\)
Its magnitude is
\(|2\vec{a}+\vec{b}| = \sqrt{1+16+64}\)
\( = \sqrt{81} = 9\)