Question

Find the point closest to the origin in the line of intersection of the planes y + 2z = 10 and x + y = 11. The point closest to the origin is . (Type an ordered triple.)

Answer 1

Answer with explanation:

The equation of two planes are

  1.→y +2 z=10

   2.→x+y=11

To find the point of Intersection of two planes

let,→ y=t

→2 z=10 - t

10 -2 z=t

→x=11 -t

11 -x=t

So,Writing equation of line which is intersection of two planes

    → 11 -x = y= 10-2 z=t

$\rightarrow \frac{x-11}{-1}=\frac{y}{1}=\frac{z-5}{\frac{-1}{2}}=t$

                                          ---------------------------------(1)

⇒Putting , x=0, y=0 and z=0 in the above equation ,to find the point Closest to Origin which will be

    =(11, 0, 10)