Question

Achar a distancia do ponto P ao plano pi, nos casos:

A) P(2.-1,2) Pi= 2x-2y-z+3=0

B) P(3,-1,4) Pi= x+y+z=0

C) P(1,3,-6) Pi= 4x-y+z+5=0

Answer 1

Para achar a distância do ponto P ao plano π, basta utilizar a fórmula

d(P, π) = | ax0 + by0 + cz0 + d | / $\sqrt{a^{2} + b^{2} + c^{2} }$

A) P (2, - 1, 2) = (x0, y0, z0)

π = 2x - 2y - z + 3 = 0

d = | 2(2) - 2(- 1) - 1(2) + 3| / √2² + 2² + (- 2)²

d = | 7 | / $\sqrt{12}$

d = 7 / $\sqrt{12}$

d = 2,02

B) P (3, - 1, 4)

π = x + y + z = 0

d = | 1(3) + 1(- 1) + 4 + 0 | / √1² + 1² + 1²

d = | 6 | / $\sqrt{3}$

d = 6 / $\sqrt{3}$

d = 3,46

C) P (1, 3, - 6)

π = 4x - y + z + 5 = 0

d = | 4(1) - 1(3) + (- 6) + 5 | / √4² + (- 1)² + (-6)²

d = | 0 | / $\sqrt{53}$

d = 0 / $\sqrt{53}$

d = 0