Question 166636: Find c so that the vectors v = i + j and w = i + c j are orthogonal
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! 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)
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