Question

Find the magnitude of the sum of these two vectors:​

Answer 1

Answer:

Explanation:

You can decompose those vectors into their components in x and y direction. For the first vector:

$\vec{r}_{1}=r_{1}\cos 30\hat{i}+r_{1}\sin 30\hat{j}=3.14(\frac{1}{2}\sqrt{3}\hat{i}+\frac{1}{2}\hat{j})=1.57\sqrt{3}\hat{i}+1.57\hat{j}$

For the second vector:

$\vec{r}_{2}=r_{2}\cos 60\hat{i}-r_{2}\sin60 \hat{j}=1.355\hat{i}-1.355\sqrt{3}\hat{j}$

The sum of two vectors will be:

$\vec{r}=\vec{r}_{1}+\vec{r}_{2}=(1.57\sqrt{3}+1.355)\hat{i}+(1.57-1.355\sqrt{3})\hat{j}\approx 4.0711\hat{i}-0.77415\hat{j}$

The magnitude of the sum of two vectors is:

$r=\sqrt{(4.0711)^{2}+(-0.77415)^{2}}\approx 4.14$ meter