Question

If $\overrightarrow{A}+\overrightarrow{B}=2\hat{i}+6\hat{j}+11\hat{k}$ and
$\overrightarrow{A}-\overrightarrow{B}=4\hat{i}+2\hat{j}-11\hat{k}$ Then find the value of $\left|\overrightarrow{A}\right|,\left|\overrightarrow{B}\right|and\overrightarrow{A}\cdot \overrightarrow{B}?$

Answer 1

We have,

$\overrightarrow{A}+\overrightarrow{B}=2\hat{i}+6\hat{j}+11\hat{k}$ (1)

$\overrightarrow{A}-\overrightarrow{B}=4\hat{i}+2\hat{j}-11\hat{k}$ (2)

Now if we add this two vectors,

$2\overrightarrow{A}=6\hat{i}+8\hat{j}$

from above equation ,

$\overrightarrow{A}=3\hat{i}+4\hat{j}$

Putting this in equation 1,

$\overrightarrow{B}=-\hat{i}+2\hat{j}+11\hat{k}$

Therefore,

$\mid A\mid =\sqrt{25}=5$

$\mid B\mid =\sqrt{126}$

And

$A\cdot B=5$