You are given two vectors A⃗ =−3.00i^+7.00j^ and B⃗ =5.00i^+2.00j^. Let counterclockwise angles be positive. 1- What angle θA, where 0∘≤θA<360∘, does A⃗ make with the +x-axis?
2-What angle θB, where 0∘≤θB<360∘, does B⃗ make with the +x-axis?
Express your answer in degrees.
3-Vector C⃗ is the sum of A⃗ and B⃗ , so C⃗ =A⃗ +B⃗ . What angle θC, where 0∘≤θC<360∘, does C⃗ make with the +x-axis?
Express your answer in degrees

1) The solution is .

2) The solution is .

3) The solution is .

1) In this case, we can determine the angle, measured in sexagesimal degrees, with respect to the x-axis by definition of dot point:

(1)

Where and are the norms of and .

If we know that and , then the angle that make with the x-axis is:

The solution is .

2) In this case, we can determine the angle, measured in sexagesimal degrees, with respect to the x-axis by definition of dot point:

(1)

Where and are the norms of and .

If we know that and , then the angle that make with the x-axis is:

The solution is .

3) In this case, we need to find the value of by vectorial sum before calculating the angles with respect to x-axis:

In this case, we can determine the angle, measured in sexagesimal degrees, with respect to the x-axis by definition of dot point:

(1)

Where and are the norms of and .

If we know that and , then the angle that make with the x-axis is:

The solution is .

We kindly invite you to see this question related to angles and dot product: link

Ax = -3       By= 7         tan phi =  -7 / 3    phi = -66.8

Since theta is in the second quadrant   theta = 180 - 66.8 = 113.2 deg

Bx = 5        By = 2        tan theta = .4        theta = 21.8 deg

Cx = Ax + Bx = 2       Cy = Ay + By = 9

tan theta = 9 / 2 = 4.5      theta = 77.5 deg

b.

explanation:

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