Question

Find the sum of vector 10i cap plus 6jcap and 4icap -2jcap

Answer 1

Given :

$\displaystyle \rm \bull \overrightarrow{A} = 10 \hat{i} + 6\hat{j }$

$\displaystyle \rm \bull \overrightarrow{B} = 4 \hat{i} - 2 \hat{j}$

To Find :

$\displaystyle \rm \overrightarrow{A} + \overrightarrow{B}$

Formula To Be Applied:

$\bull \displaystyle \rm ( x \hat{i} + y \hat{j}) + ( a \hat{i} + b \hat{j}) = (x + a) \hat{i} + ( y + b) \hat{j}$

Solution:

Let, the Resultant be :

$\displaystyle \rm \overrightarrow{r} = \overrightarrow{A} + \overrightarrow{B}$

so, we get that :

$\implies \displaystyle \rm \overrightarrow{r} = \overrightarrow{A} + \overrightarrow{B}$

$\implies \displaystyle \rm \overrightarrow{r} =( 10 \hat{i} + 6 \hat{j} )+ (4 \hat{i} - 2 \hat{j})$

$\implies \displaystyle \rm \overrightarrow{r} =( 10 + 4) \hat{i}+ (6 - 2) \hat{j}$

$\red{ \underline{ \boxed{ \implies \displaystyle \rm \overrightarrow{r} = 14 \hat{i}+ 4\hat{j}}}}$

So, the sum of the vectors is :

$\displaystyle \rm \overrightarrow{A} + \overrightarrow{B} = 14 \hat{i} + 4 \hat{j}$