Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

I am a little stuck on a problem I'm trying to solve for something I'm programming.

I'm trying to find the point at which a line meets a plane.

The line is defined as [itex]\vec{x} = \vec{a}+d\vec{l}[/itex]

where [itex]\vec{a}[/itex] is a point on the line, [itex]\vec{l}[/itex] is a unit vector defining the direction of the line and d is the distance along the line.

The plane is defined using a point [itex]\vec{x_{0}}[/itex] and normal [itex]\vec{n}[/itex] as [itex]\vec{n}.\left(\vec{x}-\vec{x_{0}}\right)=0[/itex]

I want to sub in my line equation into my plane equation and solve for [itex]d[/itex] to get [itex]\vec{x}[/itex] but my vector algebra isveryrusty and I cant for the life of me figure out how to get my [itex]d[/itex] out.

The funny thing is I used a similar method to find where a line intersects a sphere with equation [itex]\left|\vec{x}-\vec{c}\right|^{2}=R^{2}[/itex] ([itex]\vec{c}[/itex] = centre, [itex]R[/itex] = radius) and subbed in no problems. But that dot product in the plane equation is just confusing me.

Has anyone got any suggestions for me to follow?

Many thanks!

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# A 'simple' vector problem - where a line meets a plane

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