The magnitude of vectors OA → ,   OB → and OC → in the given figure are equal. The direction of OA → + OB → - OC → with x - axis will be:

Question

The magnitude of vectors OA &#8594; , &#160; OB &#8594; and OC &#8594; in the given figure are equal. The direction of OA &#8594; + OB &#8594; - OC &#8594; with x - axis will be:

Aicharya · Accepted Answer

From the above diagram, the equations are,
$\vec{OA} = R [\cos 30^{\circ} \hat{i} + \sin 30^{\circ} \hat{j}]$

$\vec{OB} = R [\cos 60^{\circ} \hat{i} - \sin 60 ° \hat{j}]$

$\vec{OC} = R [- \cos 45 ° \hat{i} + \sin 45 ° \hat{j}]$

$\Rightarrow \vec{OA} + \vec{OB} - \vec{OC} = R [\frac{1}{2} + \frac{\sqrt{3}}{2} + \frac{1}{\sqrt{2}}] \hat{i} + R [\frac{1}{2} - \frac{\sqrt{3}}{2} - \frac{1}{\sqrt{2}}] \hat{j}$ , angle with the $x -$ axis.

$\Rightarrow \tan α = \frac{\frac{1}{2} - \frac{\sqrt{3}}{2} - \frac{1}{\sqrt{2}}}{\frac{1}{2} + \frac{\sqrt{3}}{2} + \frac{1}{\sqrt{2}}} = \frac{1 - \sqrt{3} - \sqrt{2}}{1 + \sqrt{3} + \sqrt{2}}$

$\Rightarrow α = \tan^{- 1} [\frac{1 - \sqrt{3} - \sqrt{2}}{1 + \sqrt{3} + \sqrt{2}}]$ .

The magnitude of vectors OA → ,   OB → and OC → in the given figure are equal. The…

Solution

The magnitude of vectors OA &#8594; , &#160; OB &#8594; and OC &#8594; in the given figure are equal. The…

Solution

The magnitude of vectors OA → , OB → and OC → in the given figure are equal. The…