SOLUTION: Find the dot product v . w and state whether the vexctors are parallel, orthognonal, or neither: v = i + j and w = - i + j

Algebra ->  Vectors -> SOLUTION: Find the dot product v . w and state whether the vexctors are parallel, orthognonal, or neither: v = i + j and w = - i + j       Log On


   

Question 166635: Find the dot product v . w and state whether the vexctors are parallel, orthognonal, or neither:
v = i + j and w = - i + j
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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:



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