given that u=(-3,4) and vector v has an initial point of (7,0) and a terminal point of (-5,2), find 2v-3u and express your answer as a linear combination of i and j
To find 2v-3u, we first need to calculate the components of vector v and u.
Vector v = (-5 - 7, 2 - 0) = (-12, 2)
Vector u = (-3, 4)
Now, we can calculate 2v-3u:
2v = 2(-12, 2) = (-24, 4)
3u = 3(-3, 4) = (-9, 12)
Therefore, 2v - 3u = (-24, 4) - (-9, 12) = (-24 + 9, 4 - 12) = (-15, -8)
So, 2v - 3u = -15i - 8j.