Show that t

Formula : Plane = r . (n) = d

Where r = any random point

n = normal vector of plane

d = distance of plane from origin

If two planes are parallel , then their normal vectors are either same or proportional to each other

Therefore ,

Plane 1 : - 2x – y + 6z = 5

Normal vector (Plane 1) = (2i – j + 6k) …..(1)

Plane 2 : - 5x – 2.5y + 15z = 12

Normal vector (Plane 2) = (5i – 2.5j + 15k) …..(2)

Multiply equation(1) by 5 and equation(2) by 2

Normal vector (Plane 1) = 5(2i – j + 6k)

= 10i – 5j + 30k

Normal vector (Plane 2) = 2(5i – 2.5j + 15k)

= 10i – 5j + 30k

Since, both normal vectors are same .Therefore both planes are parallel