Find the points of intersection of the line x = 3+2t, y =5+7t, z = -3+t, that is, I(t) = 3+2t, 5+7t, -3+t, with the coordinate planes.

Tabansi 2020-10-27 Answered

Find the points of intersection of the line x=3+2t,y=5+7t,z=3+t, that is, I(t)=3+2t,5+7t,3+t, with the coordinate planes.

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Expert Answer

yunitsiL
Answered 2020-10-28 Author has 108 answers

The equations of the coordinate planes is given below:
yz:x=0,zx:y=0,xy:z=0
Consider in xy plane z=0.
Substitute 0 for z in the equation of line as given below,
z=03+t=0
t=3, now x=3+2t
At t=3,
x=3+23=3+6=9
At t=3, y=5+73=5+21=26
Point is (9,26,0)
Consider in yz plane x=0.
Substitute 0 for x in the equation of line as given below,
x=03+2t=0
2t=-3. now
At t=32
y=5+7(32)=10212=112
At t=32
z=332=632=92
Point is (0,112,92)
Consider in zx plane y=0.
Substitute 0 for y in the equation of line as given below,
y=05+7t=0
7t=-5, now
At t=57
x=3+2(57)=21107=117
At t=57
z=357=2157=267
Point is (117,0,267)
Thus, the point of intersections on the coordinate planes are as given below:
xy:(9,26,0)
yz:(0,112,92)
zx:(117,0,267)

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