FINDING MAGNITUDE AND DIRECTION ANGLE OF A VECTOR

Find the following information for each vector: Graph, component form, magnitude and direction angle.

Problem 1 :

Solution:

Component form:

(R₁, R₂) = (7, 2) and (S₁, S₂) = (-1, -10)

V = <S₁ - R₁, S₂ - R₂>

V = <(-1 - 7), (-10 - 2)>

V = <-8, -12>

Magnitude:

Direction angle:

We know that (-8, -12) lies in quadrant III. Thus, the direction of the given vector is

θ = α + 180°

θ = 56.31° + 180°

θ = 236.31°

Problem 2 :

Solution:

Component form:

(P₁, P₂) = (-4, -10) and (Q₁, Q₂) = (-5, 2)

V = <Q₁ - P₁, Q₂ - P₂>

V = <(-5 + 4), (2 + 10)>

V = <-1, 12>

Magnitude:

Direction angle:

We know that (-1, 12) lies in quadrant II. Thus, the direction of the given vector is

θ = 180° - α 

θ = 180° - 85.23°

θ = 94.77°

Problem 3 :

Solution:

Component form:

(R₁, R₂) = (10, 7) and (S₁, S₂) = (-5, -3)

V = <S₁ - R₁, S₂ - R₂>

V = <(-5 - 10), (-3 - 7)>

V = <-15, -10>

Magnitude:

Direction angle:

We know that (-15, -10) lies in quadrant III. Thus, the direction of the given vector is

θ = α + 180°

θ = 33.69° + 180°

θ = 213.69°

Problem 4 :

Solution:

Component form:

(R₁, R₂) = (-6, -4) and (S₁, S₂) = (-8, -7)

V = <S₁ - R₁, S₂ - R₂>

V = <(-8 + 6), (-7 + 4)>

V = <-2, -3>

Magnitude:

Direction angle:

We know that (-2, -3) lies in quadrant III. Thus, the direction of the given vector is

θ = α + 180°

θ = 56.31° + 180°

θ = 236.31°