Add vectors $\to A, \to B$ and $\to C$ each having magnitude of 100 unit and inclined to the X-axis at angles $45^{0}, 135^{0}$ and $315^{0}$ respectively.

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Solution

x component of $\to A$ = 100 cos $45^{0} = \frac{100}{\sqrt{2}}$ unit

x component of $\to B$ = 100 cos $135^{0} = \frac{100}{\sqrt{2}}$

x component of $\to C$ = 100 cos $315^{0}$

= 100 cos $45^{0}$ = $\frac{100}{\sqrt{2}}$

Reulstant x component

= $\frac{100}{\sqrt{2}} - \frac{100}{\sqrt{2}} + \frac{100}{\sqrt{2}} = \frac{100}{\sqrt{2}}$

Now, y component of $\to A$ = 100 sin $45^{0} = \frac{100}{\sqrt{2}}$

y comoponent of $\to B$ = 100 sin $135^{0} = \frac{100}{\sqrt{2}}$

y comoponent of $\to C$ = 100 sin $135^{0} = \frac{100}{\sqrt{2}}$

Resultant y component

= $\frac{100}{\sqrt{2}} + \frac{100}{\sqrt{2}} - \frac{100}{\sqrt{2}}$

= $\frac{100}{\sqrt{2}}$

Resultant = $\sqrt{{(\frac{100}{\sqrt{2}})}^{2} + {(\frac{100}{\sqrt{2}})}^{2}}$

= $\sqrt{10000}$ = 100

tan $α = \frac{y comp}{x comp}$

= $\frac{100 \sqrt{2}}{100 \sqrt{2}} = 1$

$\Rightarrow α = t a n^{- 1} (1) = 45^{0}$

The resultant is 100 unit, at $45^{0}$ with x axis.

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Add vectors →A,→B and →C each having magnitude of 100 unit and inclined to the X-axis at angles 450,1350 and 3150 respectively.

Add vectors $\to A, \to B$ and $\to C$ each having magnitude of 100 unit and inclined to the X-axis at angles $45^{0}, 135^{0}$ and $315^{0}$ respectively.