Give the component form of the resultant vector in the following.

Question

NOTE: Answer must be typed in using the following format -- including the parentheses: (#,#)
u = (9, 2)
v = (-5, -2)
2u - 3v = ?

Answer 1

To find 2u - 3v, we can multiply each component of u and v by the given scalars, then subtract the resulting vectors:

2u = 2 * (9, 2) = (2 * 9, 2 * 2) = (18, 4)
3v = 3 * (-5, -2) = (3 * -5, 3 * -2) = (-15, -6)

Now we can subtract these vectors:

2u - 3v = (18, 4) - (-15, -6)

To subtract vectors, we can subtract the corresponding components:

(18 - (-15), 4 - (-6)) = (18 + 15, 4 + 6) = (33, 10)

Therefore, 2u - 3v = (33, 10).