Question

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.

Answer 1

Parametric equations are

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

(i)

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

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

$Point\ C(8, 10, 0)$

ii)

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