SOLUTION: The points A, B, C and D have position vectors i +j +k, 2i+3j, 3i+5j-2k and -j+k respectively. find which of the following pairs of lines are parallel. a) AB and CD b) BC and CD

Question 1109182: The points A, B, C and D have position vectors i +j +k, 2i+3j, 3i+5j-2k and -j+k respectively. find which of the following pairs of lines are parallel. a) AB and CD b) BC and CD c) BC and AD
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Looking at the vector addition,
so

Similarly,

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A:(1,1,1)
B:(2,3,0)
C:(3,5,-2)
D:(0,-1,1)
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AB=B-A=(2,3,0)-(1,1,1)=(2-1,3-1,0-1)=(1,2,-1)
BC=C-B=(3,5,-2)-(2,3,0)=(3-2,5-3,-2-0)=(1,2,-2)
CD=D-C=(0,-1,1)-(3,5,-2)=(0-3,-1-5,1-(-2))=(-3,6,3)
AD=D-A=(0,-1,1)-(1,1,1)=(0-1,-1-1,1-1)=(-1,-2,0)
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You can either find the unit vectors of each vector and compare or you can look for vectors that are multiples of each other, where is an integer.
Upon inspection you can see that , so CD and AB are parallel.

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