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Question

How do you multiply vectors by vectors?


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Solution

We have two different methods to multiply vectors by vectors. They are:

1) Cross product

2) Dot product

1)Cross product (vector product) of two vectors is equal to the product of the magnitude of vectors and sine of the angle formed between them.

IfA andB are two vectors, then the cross product ofA andB is given by:

A×B=|A||B|sinθn^

where n^ is the unit vector, in the direction of A×B and perpendicular to A and B

2)Dot Product (scalar product) is the product of the magnitude of vectors and the cosine of the angle formed between them. IfA and B are two vectors, then the dot product of A andB is given by:

A.B=|A||B|cosθ


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