Let l be the line that passes through (3,0,2) and (2, -1, 3) a) find the paramet

Question

Let l be the line that passes through (3,0,2) and (2, -1, 3)

a) find the parametric equations for l.

b) Determine whether or not l intersects the line defined by the parematric equations

                       x=t,        y= (3/2)-2t,               z= 5-t

and if so, find the point(s) of intersection.

c) Determine whether or not l intersects the plane

                          2x+y+3z=15

and if so, find the point(s) of intersection.

I WILL RATE ASAP.

Let l be the line that passes through (3,0,2) and (2,-1,3). Find parametric equations for l. Determine whether or not l intersects the line defined by the parametric equations x=t, y=3/2-2t,z=5-t, and if so, find the point(s) of intersection. Determine whether or not l intersects the plane 2x + y + 3z = 15 and if so, find the point(s) of intersection

Explanation / Answer

a) r(t) = (3,0,2)+t( 2,-1,3)

x(t) = 3+2t
y(t) = -t

z(t) 2+3t

b) If two lines intersecting than x component will be equal to second line x component and so on
3+2*t1 = t2

-t1 = 1.5 - 2*t2

2+3*t1 = 5 - t2

t1 = -1.5 and t2 = 0 is solution. So both are intersecting at point (0,1.5,5)

C) Intersection occurs when all of the equations are simultaneously true.

Hence putting line value in plane equation

2(3+2t) -t+3(2+3t) = 15

13*t = 3

t= 3/13

Point of intersection is (45/13, -3/13 , 48/13 )

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