Question

Use the image to answer the question.Vectors u and v are graphed. Explain in detail each step necessary to find the angle between the two vectors and find the angle in degrees.

Answer 1

we have that

V(-2,-1) and U(-3,-4)

step 1

Find out the angle of the vector V with the x-axis

Let

x1 ----> angle of vector V with the x-axis

tan(x1)=1/2

x1=tan^-1(1/2)

x1=26.6 degrees

step 2

Find out the angle of the vector U with the x-axis

Let

x2 ----> angle of the vector U with the x-axis

tan(x2)=4/3

x2=tan^-1(4/3)

x2=53.1 degrees

step 3

Find out the angle between the two vectors

x2-x1=53.1-26.6=26.5 degrees

therefore

The angle between the two vectors is 26.5 degrees