It's hard to know where to start with you because you did not post anything regarding what you already know.
I'm going to assume that you know some vector basics. Did you draw a picture?
If we impose an xy-coordinate system, then we can draw a vector for the first leg of the trip beginning at the origin.
Let U be the vector for the first leg of the trip. Its components are <1.2, 0> .
The phrase "45 degrees west of north" tells us that the second leg of the trip makes a 45-degree angle with the x-axis, heading toward Quadrant II.
Call the vector representing the second leg of the trip V. Basic trigonometry gives us the components of the unit vector for V.
This unit vector has components <-sqrt(2)/2, sqrt(2)/2> .
Now we can get the components for V by multiplying the components of its unit vector by its magnitude (2.4).
V = <-1.6971, 1.6971>
Let the last leg of the trip be represented by vector W.
Since the ppl group ends up at the origin, we know that the sum of vectors U, V, and W must equal the zero vector.
Let the components of W be <a, b> . Therefore:
<1.2, 0> + <-1.6971, 1.6971> + <a, b> = <0, 0>
Is this enough information for you to determine the length and direction of the third leg of the trip? Those are the answers to the two questions which this exercise asks.
Check your textbook for examples on how to calculate the magnitude (length) of a vector from its components, if you're not sure.
Determining the direction (in degrees) of W from its components requires trigonometry. Have you studied any trigonometry?
If you need more help with this exercise, then please show whatever work you can and explain your reasoning. The more information that you post about your situation, the more I will understand how to help you.
