I have followed the instructions in my book and it does not make since.?

Question

1. A vector has the following initial and terminal points respectively:

Initial point: (-1, 2)

Terminal point: (4, 6)

What is the position vector?

2. Find the magnitude of the following vector: v = 4i - 2j

3. Find the unit vector that has the same direction as the vector v= -5j

4. In which quadrant is the terminal point of the vector v = 6i - 10j located.

5. Perform the following operation: v - w = ? where, v = 8i - 6j and w = - 2i + 4j

Answer 1

1. Position vector gives position from origin.  Used for plotting movement.

v = 4i + 6j

2. mag = √(4^2 +[-2]^2) = 4.47

3. A unit vector is a vector of length 1.  Obtained by dividing components by magnitude.  This is simple since magnitude is 5 and vector is on -j axis.

v = -j

4. Positive x and negative y, so quadrant IV (4).

5.  Subtract i and j components.

v - w = (8i - 6j) - (-2i + 4j) = 8i - 6j + 2i - 4j = 10i -10j