The scalar product of two vectors has a magnitude that is proportional to (consider θ as angle between two vectors):

The dot product of two vectors:

• The dot product or scalar product is the sum of the products of the corresponding entries of the two sequences of numbers.
• Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them.
• Let the two vectors are A and B then dot the Product of the two vectors:

A⋅B = |A||B| cos θ 

Where |A| = Magnitude of vectors A and |B| = Magnitude of vectors B and θ is the angle between A and B

Vector Product of Two Vectors:

• The vector product or cross product of two vectors is defined as a vector having a magnitude equal to the product of the magnitudes of two vectors with the sine of the angle between them, and direction perpendicular to the plane containing the two vectors in accordance with the right-hand screw rule.
• The symbol for the cross product is given by the cross sign (×).
• Let the two vectors be A and B then cross the Product of the two vectors:

A × B = |A||B| sin θ 

Where |A| = Magnitude of vectors A and |B| = Magnitude of vectors B and θ is the angle between A and B

Explanation: