Question

Two vectors are given by $\vec{A}=\left(3\hat{i} +\hat{j}+3\hat{k}\right)$ and $\vec{B}=\left(3\hat{i} +5\hat{j}-2\hat{k}\right)$. Find the third vector $\vec{C}$ if $\vec{A}+3\vec{B}-\vec{C}=0.$

• A. $\left(12 \hat{i}+14 \hat{j}+12 \hat{k}\right)$
• B. $\left(13 \hat{i}+17 \hat{j}+12 \hat{k}\right)$
• C. $\left(12 \hat{i}+16 \hat{j}-3 \hat{k}\right)$
• D. $\left(15 \hat{i}+13 \hat{j}+4 \hat{k}\right)$

Answer 1

Answer: (C)

$\left(12 \hat{i}+16 \hat{j}-3 \hat{k}\right)$

Answer 2

$\vec{A}+3\vec{B}-\vec{C}=0$
$3\hat{i}+\hat{j}+3\hat{k}+3\left(3 \hat{i}+5\hat{j}-2 \hat{k}\right)-\vec{C}=0$
$12 \hat{i}+16 \hat{j}-3 \hat{k}-\vec{C}=0$,
$\vec{C}=12 \hat{i}+16 \hat{j}-3 \hat{k}$