Question

what is dot product and what is cross product.....
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Answer 1

Dot Product : The product between any two vectors that gives a scalar quantity is called dot product . Since , it results in a scalar quantity , it is also called scalar product .

For example : Work is the dot product of two vectors force and displacement . Dot product involves the cosine of the angle between the two vectors . Suppose for any two vectors $\vec{A}$ and $\vec{B}$ , the dot product is given by :

$\vec{A} . \vec{B} = AB cos\theta$

Cross product : The product between any two vectors that gives a vector quantity is called cross product . It is also called vector product as the resultant is a vector quantity .

For example : Torque is the cross product of force and perpendicular distance between the axis of rotation and line of action of force . Cross product involves sine of angle between the two vectors . Suppose for any two vectors $\vec{A}$ and $\vec{B}$ , the cross product is given by :

$\vec{A} \times \vec{B} = AB sin\theta \hat{n}$ , where n is a unit vector .

It is not commutative because it involves the direction .

Answer 2

Answer:

$\huge{\boxed{\mathcal\pink{\fcolorbox{red}{purple}{Dot product}}}}$

The scalar product or dot product of two vectors is defined as the product of the magnitudes of both the vectors ant the cosine of the angle between them.

$\huge{\boxed{\mathcal\pink{\fcolorbox{red}{purple}{Cross product}}}}$

The vector product or cross product of two vectors is defined as another vector having a magnitude equal to the product of the magnitudes of two vectors and the sine of the angle between them.

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