You are given two vectors A⃗ =−3.00i^+5.00j^ and B⃗ =7.00i^+2.00j^. Let counterclockwise angles be positive. a)What angle θA, where 0∘≤θA<360∘, does A⃗ make with the +x-axis?
Express your answer in degrees.

b)What angle θB, where 0∘≤θB<360∘, does B⃗ make with the +x-axis?
Express your answer in degrees.

c)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.

Explanation:

We can subtract directly the corresponding components and check using the parallelogram rule.

Explanation:

Have a look:

enter image source here

Where, graphically, I used the fact that:

→

A

−

→

B

=

→

A

+

(

−

→

B

)

For the magnitude we use Pythagoras (with the components) to get:

∣

∣

∣

→

A

−

→

B

∣

∣

∣

=

√

(

−

1

)

2

+

(

5

)

2

=

√

1

+

25

=

√

26

≈

5.1

For the direction I can see that will be

90

∘

from the

x

axis up to the

y

axis, plus the little bit passed the

y

axis given as:

θ

=

arctan

(

1

5

)

=

11.3

∘

giving in total: angle

=

90

∘

+

11.3

∘

=

101.3

∘

answer(20) psi;