Question 166635
Since v = i + j   and   w  =  - i + j, this means that v=<1,1> and w=<-1,1>



So their dot product is 


v · w = 1*1+1*(-1) = 1 - 1 = 0



Since their dot product is equal to zero, this means that the two vectors are orthogonal (perpendicular)



Here's a picture to help visualize the problem and verify the answer:




<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/orthogonalvectors.png" alt="Photobucket - Video and Image Hosting">