If a=(5,2) and b=(-3,1) then which of the following vectors represent 3a-2b?
a) (9,4)
b) (9,8)
c) (21,8)
d) (21,4)
what are your thoughts on this one?
3a = (15, 6). 2b = (-6, 2)
3a-2b = (15, 6)-(-6, 2) = (21, 4).
To find the vector representation of 3a-2b, we need to multiply the vector a by 3 and the vector b by 2, and then subtract the results.
Given that a = (5,2) and b = (-3,1), we can compute 3a as follows:
3a = (3 * 5, 3 * 2) = (15, 6)
Similarly, we can compute 2b as follows:
2b = (2 * -3, 2 * 1) = (-6, 2)
Now, to find 3a - 2b, we subtract the individual components:
3a - 2b = (15 - (-6), 6 - 2) = (21, 4)
So, the correct option is d) (21,4).