# The sum of two vector A and B is 5i+j and their difference is 3i-2j the vector then is?

Aug 9, 2018

The vectora are $\vec{A} = \left(4 \hat{i} - \frac{1}{2} \hat{j}\right)$ and $\vec{B} = \left(\hat{i} + \frac{3}{2} \hat{j}\right)$

#### Explanation:

The sum is

$\vec{A} + \vec{B} = 5 \hat{i} + 1 \hat{j}$

The difference is

$\vec{A} - \vec{B} = 3 \hat{i} - 2 \hat{j}$

Adding the $2$ equations

$2 \vec{A} = 8 \hat{i} - 1 \hat{j}$

$\vec{A} = \frac{1}{2} \left(8 \hat{i} - 1 \hat{j}\right) = 4 \hat{i} - \frac{1}{2} \hat{j}$

Subtracting the $2$ equations

$2 \vec{B} = 2 \hat{i} + 3 \hat{j}$

$\vec{B} = \frac{1}{2} \left(2 \hat{i} + 3 \hat{j}\right) = \hat{i} + \frac{3}{2} \hat{j}$