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  • If  are unit vectors such that <img alt="(\vec{a}+\vec{b})

If \vec{a},\; \vec{b} are unit vectors such that (\vec{a}+\vec{b}).[( 2\vec{a}+3\vec{b} )\times ( 3\vec{a}-2\vec{b})\;]=0,  then angle between  \vec{a} \; and\; \; \vec{b} is -

Option: 1

0


Option: 2

\frac{\pi }{2}


Option: 3

\pi


Option: 4

Indeterminate


Answers (1)

best_answer

As we have learnt in

 

Scalar, Dot or Inner Product -

Scalar product of two vectors & \vec{B} written as \vec{A} \cdot \vec{B} is a scalar quantity given by the product of the magnitude of \vec{A} & \vec{B} and the cosine of the smaller angle between them.

\vec{A}\cdot \vec{B}= AB \cos \theta\vec{A}\cdot \vec{B}= AB \cos\theta

- wherein

showing the representation of scalar products of vectors.

Vector or cross product -

Vector or cross product of two vectors & \vec{B} written asA\times B is a single vector whose magnitude is equal to the product of the magnitude of \vec{A} & \vec{B} and the sine of the smaller angle \theta  between them.

\vec A\times \vec B= A\, B\sin \theta

- wherein

The figure shows the representation of vectors or cross product of vectors.

shows representation of vector or cross product of vectors

0=\left ( \vec{a}+\vec{b} \right ).\left ( 2\vec{a}+3\vec{b} \right )\times \left ( 3\vec{a}-2\vec{b} \right )=0

0=\left ( \vec{a}+\vec{b} \right ).\left ( -4\vec{a}\times \vec{b} -9\vec{a}\times \vec{b}\right )=-13.\left ( \vec{a}+\vec{b} \right ).\left ( \vec{a}\times \vec{b} \right )

which is true for all values of  \vec{a}\; and \; \vec{b}.

Posted by

Ritika Kankaria

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