Question

Find the resultant of the given vectors.

• A.
• B.
• C.
• D. Cannot add as is not on origin

Answer 1

The correct option is A

Let's resolve vectors along the x and y coordinates Vector A

Component of $\overrightarrow{A}$ along -ve x-axis is $4cos{30}^{\circ }=2\sqrt{3}$

But since along -ve x-axis so its $-2\sqrt{3}\hat{i}$

Component od $\overrightarrow{A}$ along +ve y-axis is $4sin{30}^{\circ }=2$

Since along +ve x-axis, so its $+2\hat{j}$

$\Rightarrow \overrightarrow{A}=-2\sqrt{3}\hat{i}+2\hat{j}$

Similarly $\overrightarrow{B}=-8cos{60}^{\circ }\hat{i}-8sin{60}^{\circ }\hat{j}$

$\overrightarrow{B}=-4\hat{i}-4\sqrt{3}\hat{j}$

$\overrightarrow{C}=5cos{45}^{\circ }\hat{i}-5sin{45}^{\circ }\hat{j}$

=$\frac{5}{\sqrt{2}}\hat{i}-\frac{5}{\sqrt{2}}\hat{j}$

$\overrightarrow{D}=\frac{3}{\sqrt{2}}\hat{i}+\frac{3}{\sqrt{2}}\hat{j}$

Now we need $\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}+\overrightarrow{D}$

Here $\overrightarrow{C}$is delocalized vector.

So we can move C any where

$\overrightarrow{A}=-2\sqrt{3}\hat{i}+2\hat{j}$

$\overrightarrow{B}=-4\hat{i}-4\sqrt{3}\hat{j}$

$\overrightarrow{C}=\frac{5}{\sqrt{2}}\hat{i}-\frac{5}{\sqrt{2}}\hat{j}$

$\overrightarrow{D}=\frac{3}{\sqrt{2}}\hat{i}+\frac{3}{\sqrt{2}}\hat{j}$

$\overrightarrow{r}=(-2\sqrt{3}-4+4\sqrt{2})\hat{i}+(2-4\sqrt{3}-\sqrt{2})\hat{j}$