Find A Vector Parallel To The Line Of Intersection Of The Planes

That you can do by setting one of the variables to 0 and solving it. L 1 3i j 2k l 2 2i j 4k. Find a vector parallel to the line of intersection of the planes given by the equations 2x 3y 5z 2 and 4x y 3z 7.
find a vector parallel to the line of intersection of the planes find a vector parallel to the line of intersection of the planes calculator


Then the equation of the line is 5 2 11 3 1 6 t a.

Find a vector parallel to the line of intersection of the planes. The general vector direction of the perpendicular lines to the first and second planes are the coefficients x y and z of the planes equations. Adding the two equations i choose the two points of intersection of the planes to be p 3 1 6 and x 5 2 11. Line of intersection of the two planes is perpendicular to both vectors. If not find the equation of the line of intersection in parametric and symmetric form.

So the vector t a 2 1 5. Then you find vector parallel to the line. Next we nd the direction vector d for the line of intersection by computing d n. To find direction vector of this line simply take the cross product of the two vectors above.

Simply you find a point where the line of intersection intersects with one of the planes x y y z x z it must with at least one of them. The given planes are 2 x y z 1 and 3 x y z 2. First we read o the normal vectors of the planes. A find a vector parallel to the line of intersection of the planes 5x 2y 2z 5 and 2x 2y 4z 0.

The intersection line can also be found by vector method. Find a vector equation of the line of intersections of the two planes x 1 5x 2 3x 3 11 and 3x 1 2x 2 2x 3 7. 4 3 5 x 2 4 1. The normal vector n 1 of x 1 5x 2 3x 3 11 is 2 4 1 5 3 3 5 and the normal vector n 2 of 3x 1 2x 2 2x 3 7 is 2 4 3 2 2 3 5.

Then find a vector parametric equation for the line of intersection. V b show that the point 1 1 1 lies on both planes. Are the planes 2x 3y z 4 and x y z 1 parallel. The cross product is used.

3 3 1 x 3 2 2 7 6 3. Favorite answer the cross product of the normal vectors of the two planes will be parallel to the line of intersection.

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Misc 15 Plane Intersection Of Planes Parallel To X Axis

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Line Of Intersection Of Two Planes Youtube

Line Of Intersection Of Two Planes Youtube

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