Answer:
r = p - q
Step-by-step explanation:
Write the two given vectors using i and j components.
i = unit vector in x direction
j = unit vector in y direction
p = -i - 3j
q = 3i - 4j
Now how can you combine these two vectors and get r when
r = -4i + j?
Adding p and q gives this:
p + q = -i - 3j + 3i - 4j = 2i - 7j
That is not r, so the addition of the vectors p and q does not work.
How about subtraction?
Start with -i from p and subtract 3i from q. You do get -4i which is the x-component of r.
Then start with -3j from p and subtract -4j from q. You get -3j - (-4j) = -3j + 4j = j which is the y-component of r.
That subtraction works.
p - q = -i - 3j - (3i - 4j) = -i - 3j - 3i + 4j = -4i + j which is exactly what r is.
Answer: r = p - q
