Question

A vector A with an x-component of 6.00 and a y-component of -4.40 is added to a vector B with x-component 3.30 and a y-component of -5.60. What is the magnitude of the resultant vector? Use proper significant figures.

Answer 1

Answer:

The magnitude of the resultant vector is 13.656 units.

Explanation:

The vector A can be represented vectorially as

 $\overrightarrow{r}_{a}=6.00\widehat{i}-4.40\widehat{j}$

Similarly vector B can be represented vectorially as

$\overrightarrow{r}_{b}=3.30\widehat{i}-5.60\widehat{j}$

Thus upon adding the 2 vectors we get

$\overrightarrow{r}_{a}+\overrightarrow{r}_{b}=6.00\widehat{i}-4.40\widehat{j}+3.30\widehat{i}-5.60\widehat{j}\\\\=(6.00+3.30)\widehat{i}-(4.40+5.60)\widehat{j}\\\\=9.30\widehat{i}-10.00\widehat{j}$

Now the magnitude of the vector is given by:

|r|=$\sqrt{x^{2}+y^{2}}\\\\|r|=\sqrt{9.30^{2}+(-10)^{2}}\\\\\therefore |r|=13.65units$