Question 166636
The vectors are orthogonal if their dot product is 0. So in this case v=<1,1> and w=<1,c>


Now take the dot product:


v · w = 1*1+1*c = 1+c



Now set the dot product equal to zero



1+c=0



Now solve for c


c=-1


So if c=-1, then the dot product will be zero. This means that if c=-1, then v and w are orthogonal



If this is hard to grasp, draw a picture of the vectors and you'll see that the two vectors  <1,1> and <1,-1> are orthogonal (perpendicular)