Question

Vector u has an initial point at (6, 8) and a terminal point at (3, -2). Vector v has an initial point at (-4, -3) and a terminal point at (1, -7). What is u - v in component form?

A) (-8, 6)
B) (-2, -6)
C) (8, 6)
D) (12, 16)

Answer 1

To calculate u - v, we find the component forms of u and v by subtracting the initial points from the terminal points of each and then subtract v from u, resulting in answer choice A) (-8, 6), recognizing a typo in the options for the y-component.

Step-by-step explanation:

To find u - v in component form, we need to first determine the component form of each vector by subtracting the coordinates of the initial point from the terminal point. For vector u, this gives us (3 - 6, -2 - 8) = (-3, -10), and for vector v, we get (1 - (-4), -7 - (-3)) = (5, -4).

Now, to find u - v, we subtract the components of v from the components of u. This results in (-3 - 5, -10 - (-4)) = (-8, -6), which is option A) (-8, 6), where there appears to be a typo in the options list provided.