Line of intersection of two planes

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Q7, the line of intersection passes through both planes.

therefore the line of intersection is perpendicular to both the normal of plane 1 and the normal of plane 2. So (normal of plane 1) x (normal of plane 2) = vector v (which passes through the intersection)

Having calculated the vector passing through the line of Intersection to be (6,-2,4), how do I progress from here to get the equation of the line of intersection?

Thanks

Posted from TSR Mobile

Reply 1

ghostwalker

17

Original post by sabre2th1

Q7, the line of intersection passes through both planes.

therefore the line of intersection is perpendicular to both the normal of plane 1 and the normal of plane 2. So (normal of plane 1) x (normal of plane 2) = vector v (which passes through the intersection)

Having calculated the vector passing through the line of Intersection to be (6,-2,4), how do I progress from here to get the equation of the line of intersection?

Thanks

Posted from TSR Mobile

Since the question is couched in coordinate geometry rather than vectors, I'd use stick with that.

From the equations of the two planes, eliminate one of the variables (z say, though it doesn't usually matter), you'll then get x in terms of y. Substitute back into one of the equations and you'll get z in terms of x or y (not both).

You're now in a position to write the equation of the line.

Reply 2

brianeverit

9

Original post by sabre2th1

Q7, the line of intersection passes through both planes.

therefore the line of intersection is perpendicular to both the normal of plane 1 and the normal of plane 2. So (normal of plane 1) x (normal of plane 2) = vector v (which passes through the intersection)

Having calculated the vector passing through the line of Intersection to be (6,-2,4), how do I progress from here to get the equation of the line of intersection?

Thanks

Posted from TSR Mobile

If you want to do it using vectors, note that

\begin{pmatrix} 3\\1\\4\end{pmatrix} \mathrm{\ and\ }\begin{pmatrix}-1\\1\\2\end{pmatrix}

are vectors normal to the p[lanes so their cross product will give you the direction of the line of intersection. You only need to find the coordinates of any point common to the two planes to complete the question.

Line of intersection of two planes

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