# Finding the line that is not parallel with others

by Jeze628   Last Updated September 12, 2019 04:20 AM

Find the line that is not parallel to the other three.

1) x = (2,0) + t(1,1)

2) x = (1,2) + t(-1,1)

3) x = (1,1) + t(1,-1)

4) x = (1,3) + t(-1,1)

Not sure how to approach this as I only know how to find parallel vectors. So how can I find parallel lines? Apparently, the line that is not parallel to the other three is option 1, which I believe is because of the point (1, 1) not being a scalar multiple of the others, but what about the other point?

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So parallel lines have the same "slope"

How can we generalize that? Well, for line 1, we go up $$1$$ on y-axis for every $$1$$ we go up on $$x$$-axis.

For the other three, we go down $$1$$ on the y-axis for every $$1$$ we go up on $$y$$-axis.

SO #1 is not parallel.

We can also see this because $$(-1,1)$$, $$(1,-1)$$, and $$(-1,1)$$ are all multiples of each other, so $$(1,1)$$ is the oddball.

Remember parallel means same slope so we're not concerned with the first term in each line expression.

You have given a pair of straight lines in each line of text. The two vectors are given by $$( u,v)+ t(a,b)$$

Parallelism depends on slope equality. So we can disregard first bracket in each case.

The relative slope we can define is then simply

$$\frac {dy/dt}{dx/dt}=b/a$$

Among the four choices the first has a relative slope $$+1$$ and the other three have $$-1$$

So the first choice is correct for parallelism.