Question

lf $\overline{A}=3\hat{i}+5\hat{j}-2\hat{k}$, and vector $\overline{B}=-3\hat{j}+6\hat{k}$. Find a vector $\overline{C}$ such that 2 $\overline{A}+7\overline{B}+4\overline{C}=0$

• A. $-6\hat{i}+11\hat{j}-38\hat{k}$
• B. $11\hat{j}-4\hat{k}$
• C. $-1.5\hat{i}+2.75\hat{j}-9.5\hat{k}$
• D. $4\hat{j}-6\hat{k}$

Answer 1

The correct option is C $-1.5\hat{i}+2.75\hat{j}-9.5\hat{k}$

$2\overrightarrow{A}+7\overrightarrow{B}+4\overrightarrow{C}=0$
$\overrightarrow{C}=\frac{-(2\overrightarrow{A}+7\overrightarrow{B})}{4}$

$2\overrightarrow{A}+7\overrightarrow{B}=6\hat{i}-11\hat{j}+38\hat{k}$

$\overrightarrow{C}=-1.5\hat{i}+2.75\hat{j}-9.5\hat{k}$