Question
Add vectors $\overrightarrow{\text{A}},\overrightarrow{\text{B}}$ and $\overrightarrow{\text{C}}$ each having magnitude of 100 unit and inclined to the X-axis at angles 45°, 135° and 315° respectively.
✓
Answer
x component of $\overrightarrow{\text{A}}=100\cos45^{\circ}=\frac{100}{\sqrt{2}}\text{ unit}$ x component of $\overrightarrow{\text{B}}=100\cos135^{\circ}=\frac{100}{\sqrt{2}}$ x component of $\overrightarrow{\text{C}}=100\cos315^{\circ}=\frac{100}{\sqrt{2}}$ Resultant x component $=\frac{100}{\sqrt{2}}-\frac{100}{\sqrt{2}}+\frac{100}{\sqrt{2}}=\frac{100}{\sqrt{2}}$ y component of $\overrightarrow{\text{A}}=100\sin45^{\circ}=\frac{100}{\sqrt{2}}\text{unit}$ y component of $\overrightarrow{\text{B}}=100\sin135^{\circ}=\frac{100}{\sqrt{2}}$ y component of $\overrightarrow{\text{C}}=100\sin315^{\circ}=\frac{100}{\sqrt{2}}$ Resultant y component $=\frac{100}{\sqrt{2}}+\frac{100}{\sqrt{2}}-\frac{100}{\sqrt{2}}=\frac{100}{\sqrt{2}}$ Resultant $=100$$\tan\alpha=\frac{\text{y component}}{\text{x component}}=1$
$\Rightarrow\alpha=\tan^{-1}(1)=45^{\circ}$
The resultant is 100 unit at 45° with x-axis.
$\Rightarrow\alpha=\tan^{-1}(1)=45^{\circ}$
The resultant is 100 unit at 45° with x-axis.
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