Answer to Question #278326 in Analytic Geometry for Ojugbele Daniel

Question #278326

Find the parametric equations for the line L through P(5,-2,4) that is parallel to (1/2, 2, -2/3)

(i) where does line L intersect the xy- plane?

(ii) sketch the position vector for a and the line L.


1
Expert's answer
2021-12-14T13:43:41-0500

Parametric equations are


x=5+12t,y=2+2t,z=423tx=5+\dfrac{1}{2}t, y=-2+2t, z=4-\dfrac{2}{3}t

(i)


z=0=>423t=0=>t=6z=0=>4-\dfrac{2}{3}t=0=>t=6

x=5+12(6)=8,y=2+2(6)=10x=5+\dfrac{1}{2}(6)=8, y=-2+2(6)=10

Point C(8,10,0)Point\ C(8, 10, 0)


ii)

The position vector is r=12,2,23\vec r=\langle\dfrac{1}{2}, 2, -\dfrac{2}{3}\rangle


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