The angle between the vectors $\overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}}\$and$\ \overrightarrow{\mathbf{a}} - \overrightarrow{\mathbf{b}}\$when$\ \overrightarrow{\mathbf{a}} = (1,1,4)$and$\ \ \overrightarrow{\mathbf{b}} = (1, - 1,4)$ is

Question

Dr. Abubacker · Accepted Answer

(b)
Here, $\left| \overrightarrow{\mathbf{a}} ight| = \sqrt{1 + 1 + (4)^{2}} = 3\sqrt{2}$
$and\ \left| \overrightarrow{\mathbf{b\ }} ight| = \sqrt{1 + ( - 1)^{2} + (4)^{2}} = 3\sqrt{2}$
$	herefore\left| \overrightarrow{\mathbf{a}} ight| = \left| \overrightarrow{\mathbf{b}} ight|$
Now, $\left( \overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}} ight) \bullet \left( \overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} ight) = {|\overrightarrow{\mathbf{a}}|}^{2} - {|\overrightarrow{\mathbf{b}}|}^{2} = 0$
Hence, angle between them is $90{^\circ}$

Q. The angle between the vectors $\overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}}\$and$\ \overrightarrow{\mathbf{a}} - \overrightarrow{\mathbf{b}}\$when$\ \overrightarrow{\mathbf{a}} = (1,1,4)$and$\ \ \overrightarrow{\mathbf{b}} = (1, - 1,4)$ is

Explanation

Reviewed by Dr. Abubacker

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