Question

Find the equation of the plane if the foot of the perpendicular from origin to the plane is

1, 3,- 5 ​

Answer 1

Answer:

General equation of plan

⇒

ax+

by+

c=

d

Given(2,3,−5)is on the plane.

2a+ 3b− 5c= d− −− −(1)

Directional ratios of the perpendicular to the plane

⇒ (a,b,c)

And the perpendicular passes through the origin.

∴equation of line

⇒

a

x−2

=

b

y−3

=

c

z+5

=

k

The line passes through origin

⇒

x=

ak+

2

y= bk+ 3

z= ck− 5

⇒ ak+ 2= 0

⇒ a= −2/k

bk+ 3= 0⇒ b= −3/k

ck− 5= 0⇒ c= 5/k

∴ equation of plane

⇒

k

−2

(x)−

k

3

y+

k

5

z= d

−2x− 3y+ 5z= dk

It passes through

(2,3,−5)

−2(2)− 3(3)+ 5(−5)= dk

−38= dk

∴ equation of plane

⇒

5z+38=2x+3y

⇒

2x+3y−5z=38

Step-by-step explanation:

i hope its helpful 4 7