If u = (1, 4, 2), v = (3, 5, 6) and w = (2, 2, 3) are three vectors in R3, then (u + v) . 5(u - w) is_____

Question

If u = (1, 4, 2), v = (3, 5, 6) and w = (2, 2, 3) are three vectors in R³, then (u + v) . 5(u - w) is_____

Answer 1

The first step is to compute (u+v) and 5(u-v).

Addition of vectors is done by adding together the entries in each position.

So, for example (1,2,3)+(1,1,0) = (1+1,2+1,3+0) = (2,3,3).

Subtraction works the same way.

So (1,2,3)-(0,1,0) = (1-0,2-1,3-0) = (1,1,3).

Multiplying a vector by a scalar is also done to each component, so 5*(1,1,3) = (5*1,5*1,5*3) = (5,5,15).

Lastly, the dot product. You multiply the components and then add them up. So (2,3,3).(5,5,15) = 2*5 + 3*5 +3*15 = 10 + 15 + 45 = 70.

I've answered the question with u=(1,2,3) and v=(1,1,0) and w=(0,1,0). By following the same procedure with the numbers in your question, you should be able to get the answer!