Question

If the positive z-axis points upward, an equation for a horizontal plane through the point (−4,0,−3) is

Answer 1

Answer-

The equation for a horizontal plane through the point (−4,0,−3) is z = -3

Solution-

Let's assume n is the normal vector for the horizontal plane < 0, 0, 1 > .

The co-ordinate of the point is (-4, 0, -3)

The general equation of a plane is -

$n \cdot = 0$

$\Rightarrow \cdot \ = 0$

$\Rightarrow 0(x+4)+0(y)+1(z+3)=0$

$\Rightarrow z=-3$

∴  The equation for a horizontal plane through the point (−4,0,−3) is z= -3