If $\overrightarrow{\mathbf{a}}\ and\ \overrightarrow{\mathbf{b}}$ are two unit vectors inclined to $x$-axis at anlges $30{^\circ}$ and $120{^\circ}$, then $|\ \overrightarrow{\mathbf{a}}\mathbf{+}\overrightarrow{\mathbf{b}}\ |$ equals

Question

Dr. Abubacker · Accepted Answer

(b)
Clearly, angle between $\overrightarrow{\mathbf{a}}\ and\ \overrightarrow{\mathbf{b}}$ $= \frac{\pi}{2}$
$\Rightarrow \ \overrightarrow{\mathbf{a}}\mathbf{\  \bullet \ }\overrightarrow{\mathbf{b}}$=0
$	herefore\left| \mathbf{\ }\overrightarrow{\mathbf{a}}\mathbf{+ \ }\overrightarrow{\mathbf{b}} ight|^{\mathbf{2}} = a^{2} + b^{2} + 2\overrightarrow{\mathbf{a}}\  \bullet \ \overrightarrow{\mathbf{b}}\$
$= 1 + 1 + 0 = 2$
$\Rightarrow \ \left| \ \overrightarrow{\mathbf{a}}\mathbf{+ \ }\overrightarrow{\mathbf{b}} ight| = \sqrt{2}$

Q. If $\overrightarrow{\mathbf{a}}\ and\ \overrightarrow{\mathbf{b}}$ are two unit vectors inclined to $x$-axis at anlges $30{^\circ}$ and $120{^\circ}$, then $|\ \overrightarrow{\mathbf{a}}\mathbf{+}\overrightarrow{\mathbf{b}}\ |$ equals

Explanation

Reviewed by Dr. Abubacker

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