DISTRIBUTIVE LAW FOR DOT PRODUCT

DISTRIBUTIVE LAW FOR DOT PRODUCT

DISTRIBUTIVE LAW FOR
DOT PRODUCT

According to distributive law for dot product:

PROOF

Consider three vectors

and

.Here we will use geometric interpretation of dot product by drawing projection as shown below. First we obtain the sum of vectors

and

by head to tail rule then we draw projection

and

from the terminal point of vector

respectively onto the direction of

.
The dot product

is equal to the projection of vector

onto the direction of

multiplied by the magnitude of

. i.e.

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