SOLUTION: show that the vectors A = 3i - 2j +k , B= i - 3j + 5k , C= 2i + j - 4k form a right angled triangle.

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Question 762394: show that the vectors A = 3i - 2j +k , B= i - 3j + 5k , C= 2i + j - 4k form a right angled triangle.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
if
A+=+3i+-+2j+%2Bk ,
B=+i+-3j+%2B+5k ,
C=+2i+%2B+j+-+4k form a right angled triangle, then they satisfy Pythagorean theorem
C%5E2=A%5E2%2BB%5E2
if
A+=+3i+-+2j+%2Bk ,
B=+i+-3j+%2B+5k ,
C=+2i+%2B+j+-+4k
A%2BB+=+C,
A, B&C represents sides of the triangle
Then
A+=+sqrt%289+%2B4+%2B1%29=sqrt%2814%29 units
B=+sqrt%281+%2B9+%2B+25%29=sqrt%2835%29
C=+sqrt%284+%2B+1+%2B16%29=sqrt%2821%29
since C%5E2=A%5E2%2BB%5E2 = > %28sqrt%2835%29%29%5E2=%28sqrt%2814%29%29%5E2%2B%28sqrt%2821%29%29%5E2
= > 35=14%2B21
= > 35=35 ...it's true, so the triangle is right angled triangle