You are given two vectors a= -3.00i^+7.00j^ and b⃗ =7.00ι^+2.00j^. let the counterclockwise angles be positive.
1)what angle does a⃗ make with the ?
2)what angle does b⃗ make with the +x-axis?
3)vector c⃗ is the sum of a⃗ and b⃗ , so c⃗ =a⃗ +b⃗ . what angle does c⃗ make with the +x-axis

1)

First we go found the value of :

a² = (-3)² + 7²

a² = 9 + 49

a² = 58

a = √59

a = 7,68 u

Now we can found the angle with the +x-axis

ax = a · cos θ

3 = 7,68 · cos θ

3 / 7,68 = cos θ

0,39 = cos θ

0,39 ·  = θ

θ = 67º <----- This is the answer

2)


First we go found the value of :

b² = 7² + 2²

b² = 49 + 4

b² = 53

b = √53

b = 7,28 u

Now we can found the angle with the +x-axis

bx = b · cos θ

7 = 7,28 · cos θ

7 / 7,28 = cos θ

0,96 · = θ

θ = 16º

For counterclockwise:

180 - 16 = 164º <----- This is the answer

3)









Now we going to found the module of C vector:

c² = 9² + 4²

c² = 81 + 16

c² = 97

c = √97

c = 9,84 u

The angle is:

Cx = C · cos θ

4 = 9,84 · cos θ

4 / 9,84 = cos θ

0,40 · = θ

θ = 66º

For counterclockwise:

180 - 66 = 114º <----- This is the answer

I hope you enjoy!

Yes