explain dot product and cross product with eg.

The dot product, also called the scalar product, of two vectors is a number (scalar quantity) obtained by performing a specific operation on the vector components.

Mathematically it is defined as,

https://s3mn.mnimgs.com/img/shared/discuss_editlive/2191102/2012_04_07_14_52_31/image4828857492334172596.jpg

Where θ is the angle between the two vectors.

The cross product is the vector product of two vectors. The cross product of two vectors is always perpendicular to the plane on which the two vectors lies.

It is given by,

https://s3mn.mnimgs.com/img/shared/discuss_editlive/2191102/2012_04_07_14_52_31/image402642836450561604.jpg

https://s3mn.mnimgs.com/img/shared/discuss_editlive/2191102/2012_04_07_14_52_31/image1688461800599577606_4279015617023776380.jpg

 

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 DOT PRODUCT : it is the product of two vectors which gives a scalar quantity . here the product is represented by a  .  ..hence its name dot product  . 

vectorA . vectorB = AB cos(theta)

ex : W = vectorF . vector S ( work which is a scalar qty is the product of force and displacement ) ...

CROSS PRODUCT : the cross product of two vectors is defined as the vector whose magnitude is equal to product of magnitudes of the two vectors and sine of the angle between them . here product is represented by X ( cross ) ...

vector A X vectorB = AB sin (theta) ncap 

ncap is the arbitrary direction 

ex : vector torque = vector r X vector F ...

hope u got it

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