Add vectors vec{A},vec{B},and vec{C},each hav | vedclass

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(A) The vectors are given by:$\vec{A} = 50(\cos 45^{\circ} \hat{i} + \sin 45^{\circ} \hat{j}) = 50(\frac{1}{\sqrt{2}} \hat{i} + \frac{1}{\sqrt{2}} \ha

Vedclass · Accepted Answer

$50$

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(A) The vectors are given by:$\vec{A} = 50(\cos 45^{\circ} \hat{i} + \sin 45^{\circ} \hat{j}) = 50(\frac{1}{\sqrt{2}} \hat{i} + \frac{1}{\sqrt{2}} \hat{j})$$\vec{B} = 50(\cos 135^{\circ} \hat{i} + \sin 135^{\circ} \hat{j}) = 50(-\frac{1}{\sqrt{2}} \hat{i} + \frac{1}{\sqrt{2}} \hat{j})$$\vec{C} = 50(\cos 315^{\circ} \hat{i} + \sin 315^{\circ} \hat{j}) = 50(\frac{1}{\sqrt{2}} \hat{i} - \frac{1}{\sqrt{2}} \hat{j})$Summing the vectors:$\vec{R} = \vec{A} + \vec{B} + \vec{C} = 50(\frac{1}{\sqrt{2}} - \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}}) \hat{i} + 50(\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} - \frac{1}{\sqrt{2}}) \hat{j}$$\vec{R} = 50(\frac{1}{\sqrt{2}} \hat{i} + \frac{1}{\sqrt{2}} \hat{j})$The magnitude of the resultant vector is:$|\vec{R}| = \sqrt{(50/\sqrt{2})^2 + (50/\sqrt{2})^2} = \sqrt{1250 + 1250} = \sqrt{2500} = 50 	ext{ units}$.

Add vectors $\vec{A}$,$\vec{B}$,and $\vec{C}$,each having a magnitude of $50 \text{ units}$ and inclined to the $X$-axis at angles $45^{\circ}$,$135^{\circ}$,and $315^{\circ}$ respectively.

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