If ${\bf{\vec a}},{\rm{\;}}{\bf{\vec b}},{\bf{\vec c}}$ and three vectors such that ${\bf{\vec a}} = {\rm{\;}}{\bf{\vec b}} + {\bf{\vec c}}$ and the angle between ${\rm{\;}}{\bf{\vec b}}{\rm{\;and\;}}{\bf{\vec c}}$ is $\frac{\pi }{2}{\rm{then\;}}$

JEE MATHEMATICS MCQ: DOT PRODUCT OF VECTORS

1 Easy

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Application +4 | -1

\mathbf{\vec a},\mathrm{\;}\mathbf{\vec b},\mathbf{\vec c}

and three vectors such that

\mathbf{\vec a} = \mathrm{\;}\mathbf{\vec b} + \mathbf{\vec c}

and the angle between

\mathrm{\;}\mathbf{\vec b}\mathrm{\;and\;}\mathbf{\vec c}

\frac{\pi }{2}\mathrm{then\;}

View answer and explanation

Correct option: A

{a^2} = {b^2} + {c^2}

Option A (

{a^2} = {b^2} + {c^2}

) is correct because it represents the Pythagorean theorem, which applies when two vectors are orthogonal.

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{\mathbf{\vec a}}

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{\mathbf{\vec a}}

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\left| {\mathbf{\vec a}} \right|

\frac{1}{4} \mathrm{~m} / \mathrm{s}

O A

O B

30^{\circ}

45^{\circ}

O B

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