Angle betwwen 2 vector?

What language was this auto-translated from?

Hi
I think question is clear?
Actually there may same translation problems.
This is natural.
(x,y)=(-3.5,-2,5) R=4.3 what is the angle between R and (+) x coordinate?
Thank you.

The angle between the line segment (0,0)-(-3.5,-2.5) and the positive x-axis is atan2(-3.5,-2.5) = -2.5213431676 radians = -144.462322208 degrees.

Hi markr,
Thank you very much for your response.
But how you found as degree i dont know way should i divide like -3.5/-2.5*180?
Can you show me the way of solution? And as i learn answer key is 216?
a.196 b.96 c.46 d36 e.216

216 degrees is equivalent to -144 degrees since they sum to 360.
The angle is found by using the arctan function. The tangent of the angle is -2.5/(-3.5). atan(2.5/3.5) = 35.5 degrees. Since the vector is in the third quadrant, you need to add 180 degrees to get 215.5.

A little different approach

Find the line between (-3.5,-2.5) and (0,0)

line is y=mx+b

now b (x intercept) is 0 as the line goes through the origin.

so
y=mx

or

-2.5=m*(-3.5) so m=-2.5/(-3.5)=5/7

Tan (phi)=m where phi is the angle of the line with the x axis

so phi=tan-1(5/7)=35.537 deg

But this is a vector in the direction of south and east of the origin so it makes a 35.537 deg angle down from the negative x axis--the negative x axis is 180 deg and downward is an addition---so the total angle is (180+35.537) deg=215.537 deg

Rap

mark and raprap thank you very much.