Collection of Maths Problems

Plane

Task number: 2353

• Variant 1

  $(2{,}4,4)$, $(3{,}4,3)$ and $(3{,}1,6)$

• Hint

  Follow the same scenario as for line interpolation.

• Resolution

  We first deduce the parametric form $\alpha: (2{,}4,4)+t(1{,}0,-1)+s(1,-3{,}2)$.

  We then eliminate parameters (in this particular case we may add all equations together).

• Result

  The equation of the plane is: $x+y+z-10=0$.

• Variant 2

  $(6{,}4,6)$, $(3{,}5,4)$ and $(5{,}2,3)$

• Result

  $x+y-z-4=0$

• Variant 3

  $(5{,}4,7)$, $(4{,}5,5)$ and $(2{,}2,6)$

• Result

  $-x+y+z-6=0$

• Variant 4

  $(6{,}3,5)$, $(3{,}2,7)$ and $(5{,}1,4)$

• Result

  $x-y+z-8=0$