Question

If $\overrightarrow{A}=2\hat{i}+7\hat{j}+3\hat{k}$ and $\overrightarrow{B}=3\hat{i}+2\hat{j}+5\hat{k}$ Find the component of $\overrightarrow{A}$ and $\overrightarrow{B}$

Answer 1

Given that,

$\overrightarrow{A}=2\hat{i}+7\hat{j}+3\hat{k}$

$\overrightarrow{B}=3\hat{i}+2\hat{j}+5\hat{k}$

Now, the component of A along B

$=\frac{\overrightarrow{A}\cdot \overrightarrow{B}}{|B|}$

$=\frac{(2\hat{i}+7\hat{j}+3\hat{k})(3\hat{i}+2\hat{j}+5\hat{k})}{\sqrt{9+4+25}}$

$=\frac{6+14+15}{\sqrt{38}}$

$=\frac{35}{\sqrt{38}}$

Now, the component of B along A

$=\frac{\overrightarrow{A}\cdot \overrightarrow{B}}{|A|}$

$=\frac{(2\hat{i}+7\hat{j}+3\hat{k})(3\hat{i}+2\hat{j}+5\hat{k})}{\sqrt{4+49+9}}$

$=\frac{6+14+15}{\sqrt{62}}$

$=\frac{35}{\sqrt{62}}$

Hence, the components of A and B are $\frac{35}{\sqrt{38}}$ and $\frac{35}{\sqrt{62}}$