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Question
Add vectors \[\vec{A} , \vec{B} \text { and } \vec{C}\] each having magnitude of 100 unit and inclined to the X-axis at angles 45°, 135° and 315° respectively.
Solution
First, we will find the components of the vector along the x-axis and y-axis. Then we will find the resultant x and y-components.
x-component of \[\vec{A} = \ A\ cos \ 45^\circ =100 \cos 45^\circ = \frac{100}{\sqrt{2}} \text { unit }\]
x-component of \[\vec{B} = \vec{B} \cos 135^\circ = - \frac{100}{\sqrt{2}}\]
x-component of \[\vec{C}\] = \[\vec{C}\] cos 315\[^\circ\]
= 100 cos 315°
\[\tan \alpha = \frac{\text { y comp}}{\text { x comp }}\]
\[ = \frac{100\sqrt{2}}{100\sqrt{2}} = 1\]
⇒ α = tan−1 (1) = 45°
∴ The magnitude of the resultant vector is 100 units and it makes an angle of 45° with the x-axis.
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