Find an equation of the plane. the plane through the point (−5, 9, 10) and perpendicular to the line x = 1 + t, y = 4t, z = 2 −

Question

leonid [27]

3 years ago

5

Find an equation of the plane. the plane through the point (−5, 9, 10) and perpendicular to the line x = 1 + t, y = 4t, z = 2 −

3t

Mathematics

1 answer:

PtichkaEL [24] · Answer 1 · 2022-01-02T02:46:57+03:00

PtichkaEL [24]3 years ago

3 0

The direction vector of the line
L: x=1+t, y=4t, z=2-3t
is <1,4,-3>
which is also the required normal vector of the plane.

Since the plane passes through point (-5,9,10), the required plane is :
Π 1(x-(-5)+4(y-9)-3(z-10)=0
=>
Π x+4y-3z=1