Practice question · Sort into groups
Two vectors are parallel when one is a scalar multiple of the other. Sort each pair.
Groups: Parallel · Not parallel
- (1, 1) and (1, -1)
- (0, 5) and (0, -2)
- (3, 6) and (1, 3)
- (1, 2) and (3, 6)
- (2, -3) and (-4, 6)
- (1, 2) and (2, 1)
Hints
- Check whether the SAME multiplier turns every component of one vector into the other.
- A negative multiplier still counts as parallel, the vectors simply point opposite ways.
Show the answer
Parallel: (1, 2) and (3, 6), (2, -3) and (-4, 6), (0, 5) and (0, -2)
Not parallel: (1, 2) and (2, 1), (1, 1) and (1, -1), (3, 6) and (1, 3)
Why
(3, 6) = 3(1, 2) and (-4, 6) = -2(2, -3), so both pairs are parallel; opposite directions still count. (0, 5) and (0, -2) both lie along the vertical axis. But (3, 6) and (1, 3) fail: the first components need a factor of 3 and the seconds a factor of 2, and swapping components as in (1, 2) and (2, 1) is never a scaling.
Practise Vectors in the Plane and Space
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