Question

Determine the magnitude of the vector sum v = v1 + v2 and the angle θx which v makes with the positive x-axis. complete both graphical and algebraic solutions.

Answer 1

Let  θ be the angle V1 makes with x axis and θ2

√√√To start, we have  

Tan θ = 3/6=1/2

From there, do some quick manipulation to find sin θ1 and cosθ1  

So we have v1= (9 cos θ1and 9 sin θ1)=(8.05,4.02)

Now, v2 makes an angle of 1800- 630=1170=θ2with x axis so we have  

V2=(12 cosθ2,12sinθ2)=(-5.45,10.69)

From there, we have  

V=v1+v2=(2.60,14.71)

Now it’s a simply a matter of finding /v/=  √2.602+14.712

=14.9

Θx=arctan(14.71/2.6)=80°

Answer 2

The magnitude is:

$|v_1 + v_2| = \sqrt{(x_1 + x_2)^2 + (y_1 + y_2)^2}$

And the angle will be:

$\theta = Atg(\frac{y_2 + y_1}{x_2 + x_1})$

How to get the magnitude and angle?

For two vectors:

v₁ = <x₁, y₁>

v₂ = <x₂, y₂>

The sum is given by:

v₁ + v₂ = <x₁ + x₂, y₁ + y₂>

The magnitude of this vector will just be:

$|v_1 + v_2| = \sqrt{(x_1 + x_2)^2 + (y_1 + y_2)^2}$

And the angle is given by the arctangent of the quotient between the y-component and the x-component, so we have:

$\theta = Atg(\frac{y_2 + y_1}{x_2 + x_1})$

If you want to learn more about vectors, you can read:

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