Question

Suppose C⃗ =A⃗ +B⃗ where vector A⃗ has components Ax = 5, Ay = 2 and vector B⃗ has components Bx = -3, By = -5. What is the direction of vector C⃗ ?

Answer 1

First, find the components of vector C (I don't know how you added the vector arrow but that's pretty cool).

Ax + Bx = Cx, Ay + By = Cy
5 + -3 = 2, 2 + -5 = -3

Vector C can be represented as 2x, -3y.

Next, using a trigonometric function tangent you may find the angle from the origin

$\theta$ = arctan(-3/2)

$\theta = -56.31$° $= -0.983$rad

Answer 2

Answer:

326,3° or 146,31°

Explanation:

So you know that A=(5,2) and B=(-3,-5)

so C is going to be=(5,2)+(-3,-5)=(2,-3)

The direction of a vector is the measure of the angle it makes with a horizontal line.  One of the following formulas can be used to find the direction of a vector:

tanα=$\frac{x}{y}$

tanα=$\frac{2}{-3}$---> arctg($\frac{2}{-3}$)=α=326,3° or 146,31°