Here is my problem:

given vectors
u=-i-5j and v=-2i+7j, find 9u-8v

I for the most part have been getting the vector questions but this one has me stumped. Should I multiply 9(-1-5) and 8(-2+7). Then subtract the two of them. I have tried doing that and the answer does not come up.

Any help is apprectiated thanks.

You need to keep the is and js in, and treat them like any other variable (in this case they are unit vectors).

so you need:

9u-8v = 9(-i-5j)-8(-2i+7j) = (-9i-45j)-(-16i+56j) = -9i-45j+16i-56j = (-9+16)i+(-45-56)j

from here you can do the arithmetic, but you can see what I've done, I've kept the i and j and treated them separately, just like you would treat x and y separately.

Hope this helps :)

If you did not understand what Capuchin said, basically:

9(-i - 5j) - 8(-2i + 7j)

Multiply out the brackets, and then solve by: adding like terms, or subtracting like terms as stated in the question.

You have to treat the vectors as normal terms that can be multiplied.