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 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

                                          ---------------------------------(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)

the equation of the parallel line would be y = 2x + 9

step-by-step explanation:

to start we need to find the slope of the original line. we can do that by looking at the coefficient of x, which is 2

since the slope of the original line is 2 and parallel lines have the same slope, we know the new line will also have 2 slope. now we can use that along with the point given in point-slope form to get the find equation.

y - y1 = m(x - x1)

y - 5 = 2(x + 2)

y - 5 = 2x + 4

y = 2x + 9