Give the component form of the resultant vector in the following.
NOTE: Answer must be typed in using the following format -- including the parentheses: (#,#)
u = (9, 2)
v = (-5, -2)
2u - 3v = ?
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).
To find the resultant vector, we can use the formula:
Resultant = 2u - 3v
First, let's calculate 2u:
2u = 2(9, 2) = (2 * 9, 2 * 2) = (18, 4)
Next, let's calculate 3v:
3v = 3(-5, -2) = (3 * -5, 3 * -2) = (-15, -6)
Now, let's subtract the calculated vectors (3v) from (2u):
(18, 4) - (-15, -6) = (18 + 15, 4 + 6) = (33, 10)
Therefore, the component form of the resultant vector 2u - 3v is (33, 10).