If $\left| {{\bf{\vec a}}} \right| = \left| {{\bf{\vec b}}} \right| = 1{\rm{\;and\;}}\left| {{\bf{\vec a}} + {\bf{\vec b}}} \right| = \sqrt 3 ,$ then the value of $\left( {3\;{\bf{\vec a}} - 4{\bf{\vec b}}} \right)\cdot\left( {2{\bf{\vec a}} + 5{\bf{\vec b}}} \right)$ is

JEE MATHEMATICS MCQ: DOT PRODUCT OF VECTORS

1 Easy

1 of 1

Application +4 | -1

\left| {\mathbf{\vec a}} \right| = \left| {\mathbf{\vec b}} \right| = 1\mathrm{\;and\;}\left| {\mathbf{\vec a} + \mathbf{\vec b}} \right| = \sqrt 3 ,

then the value of

\left( {3\;\mathbf{\vec a} - 4\mathbf{\vec b}} \right)\cdot\left( {2\mathbf{\vec a} + 5\mathbf{\vec b}} \right)

View answer and explanation

Correct option: B

- \frac{{21}}{2}

The correct answer is B (

- \frac{{21}}{2}

) because it is the result of the dot product of the two vectors, calculated using the given magnitudes and the angle between the vectors.

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O A

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30^{\circ}

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