Calculating Magnitude and Direction of Vectors

The magnitude of vector vec is the distance between the initial point A and B and the end point Q. In symbols the magnitude of vec is written as vec3

When vectors starting coordinate and ending coordinates are given then by using distance formula, magnitude of the vector can be easily find out as :

vec2

Magnitude of a Vector

vec2

Direction of a Vector

The direction of a vector is the measure of the angle it makes with x-axis. One of the formula can be used to find the direction of a vector.
vec3
Where :
where x is the horizontal change and y is the vertical change
OR
vec2
Where where ( x1 , y1 ) is the initial point and ( x2 , y2 ) is the terminal point.

So,
vec

vec

vec

vec33

vec

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