Coincident Lines

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Coincident Lines

Postby lora » Sat Apr 20, 2013 5:35 pm

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



lora
 
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Re: Coincident Lines

Postby lily » Sat Apr 20, 2013 6:07 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!
lily
 
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Re: Coincident Lines

Postby lora » Sat Apr 20, 2013 6:18 pm

Thanks Lily!!
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