Question

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

Answer 1

4.14m

Step-by-step explanation:

Answer 2

Step-by-step 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((1)/(2)√(3)\hat{i}+(1)/(2)\hat{j})=1.57√(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√(3)\hat{j}`

The sum of two vectors will be:

`\vec{r}=\vec{r}_(1)+\vec{r}_(2)=(1.57√(3)+1.355)\hat{i}+(1.57-1.355√(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