Answer to Question #259575 in Analytic Geometry for Almas

Question

Define Scalar Product its formula and its physical interpretation.

Answer 1

Solution: One of the ways in which two vectors can be combined is known as the scalar product.

Definition: The scalar product of vector a and vector b is defined to be

$\bold {a · b = |a| |b| cos θ}$

Where |a| is the modulus, or magnitude of a

|b| is the modulus, or magnitude of b

$\bold {\theta}$ is the angle between a and b. 

Note: Note that the symbol for the scalar product is the dot ·, and so we sometimes

refer to the scalar product as the dot product.

Formula: $\bold {a · b = |a| |b| cos θ}$

Physical interpretation:

1) To determine whether two given vectors are perpendicular.

2) To find the direction cosines of a given vector.

3) To explain what is meant by the vector projection of one vector onto another vector,

and describe how to compute it.

4) To calculate the work done by a given force.