scalar question question please help

[Summer5526]

stuck on this question:

the question:

a line that passes through the origin intersects a plane at point ( 1, -3, 2). if the line is perpendicular to the plane, find the scalar equation of the plane.

 

[Summer5526]

I suspect the reason no one has replied is that "scalar equation of the plane" is not standard vocabulary.
The two points $(0,0,0)~\&~(1,-3,2)$ determine a line with direction $\left<1,-3,2\right>$
with equation $\dfrac{x}{1}=\dfrac{y}{-3}=\dfrac{z}{2}$ (symmetric form) or $x(t)=t~~,y(t)=-3t~,\text{ and }z(t)=2t$ (parametric form}
Now $(x-1)-3(y+3)+2(z-2)=0$ is the equation of the plane containing two points and normal to the line.

that’s what I was saying but my teacher put this exact question on an assignment and i’ve never been so confused! thank you for your help

 

[pka]

the question: a line that passes through the origin intersects a plane at point ( 1, -3, 2). if the line is perpendicular to the plane, find the scalar equation of the plane.

I suspect the reason no one has replied is that "scalar equation of the plane" is not standard vocabulary.
The two points $(0,0,0)~\&~(1,-3,2)$ determine a line with direction $\left<1,-3,2\right>$
with equation $\dfrac{x}{1}=\dfrac{y}{-3}=\dfrac{z}{2}$ (symmetric form) or $x(t)=t~~,y(t)=-3t~,\text{ and }z(t)=2t$ (parametric form}
Now $(x-1)+(y+3)+(z-2)=0$ is the equation of the plane containing two points and normal to the line.