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Vectors, Coincident - IB Maths HL

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

and

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

and

- lora
**Posts:**0**Joined:**Wed Apr 10, 2013 7:36 pm

IB Mathematics HL – 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

into the equation of

and we have

Therefore the point lies on . As they share a common point, cannot be parallel, thus they are coincident.

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

into the equation of

and we have

Therefore the point lies on . As they share a common point, cannot be parallel, thus they are coincident.

Hope these help!

- lily
**Posts:**0**Joined:**Mon Jan 28, 2013 8:04 pm

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