Question

How do you find a vector of length 10 in the direction of vequals=left angle 3 comma negative 2 right angle3,−2​?

Answer 1

First we look for the angle of the vector, which will be given by:
tan (x) = (- 2/3)
Clearing x we have:
x = ATAN (-2/3) = - 33.69 degrees.
Which means that the angle is 33.69 degrees measured clockwise from the x axis.
Equivalently the angle is
360-33.69 = 326.31 degrees
326.31 degrees measured counterclockwise from the x axis.
The vector is then:
v = 10 (cos (326.31) i + sin (326.31) j)
answer
v = 10 (cos (326.31) i + sin (326.31) j)