Question

Activity 1. Switch from component- to magnitude-angle representation of a vector

Determine the magnitude and the angle with respective to the positive x-axis for the following vectors. Check with the simulation to confirm your result.

VECTOR	MAGNITUDE	ANGLE	MAGNITUDE	ANGLE
	Calculated		From Simulation
(25, 10)
(-10, 5)

Question: For the second vector, did you get the same angle as the simulation showed?

Answer 1

for a Vector P(x, y)

Magnitde = |P| = sqrt (x^2 + y^2)

Direction = arctan (y/x)

Now for Vector 1

P (25, 10)

|P| = sqrt (25^2 + 10^2) = 26.93

Angle = arctan (10/25) = 21.80 deg

Now for Vector 2

P (-10, 5)

|P| = sqrt ((-10)^2 + 5^2) = 11.18

Angle = arctan (5/(-10)) = -26.565 deg

Since Coordinates of Vector 2 are in 2nd quadrent, So Angle with positve x-axis will be

Angle = 180 - 26.565 = 153.435 deg

Please Upvote.

Check that you have to confirm these result by using simulation yourself.

Comment below if you have any doubt.