Hi, there-- YOUR PROBLEM: Given the vectors u = (2,7) and v = (3,1) Find 2u-3v, u+v, and 3u-4v SOLUTION: To work add and subtract vectors, you work with the x-components and y-components separately. (a) 2u-3v Multiply the x-component and the y-component of vector u by 2 to get the vector 2u. 2u = (2*2,2*7) = (4,14) Multiply both components of vector v by 3 to get vector 3v. 3v = (3*3,3*1) = (9,3) Now subtract the x- and y-compnents of 3v from those of 2u to get the components of 2u-3v. 2u - 3v = (4-9,14-3) = (-5,11) (b) u+v Add the x- and y-components of u and v separately to give the components of u+v. (u+v) = (2+3,7+1) = (5,8) (c) 3u-4v 3u = (3*2,3*7) = (6,21) 4v = (4*3,4*1) = (12,4) 3u-4v = (6-12,21-4) = (-6,17) I hope this helps. Feel free to email if you have questions about the explanation. Mrs. Figgy math.in.the.vortex@gmail.com