If $\overrightarrow{\mathbf{a}}$ and $\overrightarrow{\mathbf{b}}$ are unit vectors and $\left| \overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}} \right| = 1$, then $\left| \overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}} \right|$is equal to

Question

Dr. Abubacker · Accepted Answer

(d)
$Given,\ \left| \overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}} \right| = 1,\ \left| \overrightarrow{\mathbf{a}} \right| = \left| \overrightarrow{\mathbf{b}} \right| = 1$
$\Longrightarrow \left| \overrightarrow{\mathbf{a}} \right|^{2} + \left| \overrightarrow{\mathbf{b}} \right|^{2} + 2\left| \overrightarrow{\mathbf{a}} \right|\left| \overrightarrow{\mathbf{b}} \right| = 1$
$\Longrightarrow 2\left| \overrightarrow{\mathbf{a}} \right|\left| \overrightarrow{\mathbf{b}} \right| = - 1\ \ \ldots(i)$
Now, $\left| \overrightarrow{\mathbf{a}} - \overrightarrow{\mathbf{b}} \right|^{2} = \left| \overrightarrow{\mathbf{a}} \right|^{2} + \left| \overrightarrow{\mathbf{b}} \right|^{2} - 2\left| \overrightarrow{\mathbf{a}} \right|\left| \overrightarrow{\mathbf{b}} \right|$
$= 1^{2} + 1^{2} - ( - 1) = 3\ \ \$[from Eq. (i)
$\Longrightarrow \ \left| \overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}} \right| = \sqrt{3}$

Q. If $\overrightarrow{\mathbf{a}}$ and $\overrightarrow{\mathbf{b}}$ are unit vectors and $\left| \overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}} \right| = 1$, then $\left| \overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}} \right|$is equal to

Explanation

Reviewed by Dr. Abubacker

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