Parallel Vectors?

Are vector AB and CD parallel?


A=(2,4,6) B=(3,4,1) C=(4,1,3) and d=(5,1,-2)





And before you ask, we haven't learned the dot product. Is there another way to figure it out?

Parallel Vectors?
Yes. They happen to be the same vector, so they are parallel.





AB = (3 - 2, 4 - 4, 1 - 6) = (1,0,-5)


CD = (5 - 4, 1 - 1, -2 - 3) = (1, 0, -5)





Also, if they have the same unit vector, they will be parallel.
Reply:AB Vector is (3-2, 1-1, 6-1) = (1,0,-5)


CD Vector is (5-4,1-1,-2-3) = (1,0,-5)


Yes!!! Parallel.
Reply:AB = (3 - 2, 4 - 4, 1 - 6) = (1, 0, -5)





CD =(5- 4,1 - 1, -2 - 3) = (1, 0, -5)





Since one is a scalar multiple of the other, these two are parallel.





CD = 1 *AB
Reply:yes