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IB Mathematics SL – Vectors, Parallel, coincident or skew lines

How can we determine if the following lines intersect in one point, are parallel and distinct, are coincident, or are skew?

and

Thanks

How can we determine if the following lines intersect in one point, are parallel and distinct, are coincident, or are skew?

and

Thanks

- Jack
**Posts:**0**Joined:**Mon Jan 28, 2013 8:08 pm

IB Mathematics SL – Vectors, Parallel, coincident or skew lines

We first rewrite the Cartesian equation for

We observe that the lines have parallel direction vectors since

Thus the lines are either parallel or coincident.

For example the point

lies on for

. Then we check whether it is also on

Set

So there is not common solution for

Therefore the lines are parallel.

Hope these help!

We first rewrite the Cartesian equation for

We observe that the lines have parallel direction vectors since

Thus the lines are either parallel or coincident.

For example the point

lies on for

. Then we check whether it is also on

Set

So there is not common solution for

Therefore the lines are parallel.

Hope these help!

- miranda
**Posts:**268**Joined:**Mon Jan 28, 2013 8:03 pm

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