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    symmetric equations for the line of intersection

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    Find symmetric equations for the line of intersection of the planes and find the angle between the planes.

    x - 2y + z = 1, 2x + y + z = 1

    © BrainMass Inc. brainmass.com December 24, 2021, 7:35 pm ad1c9bdddf
    https://brainmass.com/math/symmetric-equations-line-intersection-201051

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    Find symmetric equations for a line
    Find symmetric equations for the line of intersection of the planes and find the angle between the planes.

    x - 2y + z = 1, 2x + y + z = 1

    (a) First a point on the line must be found. By setting z = 0, we will find the point where the line intersects the x-y plane.
    x - 2y = 1
    2x + y = 1
    Solve the above equations to find the intersection point in xy plane:

    Therefore, the line intersects the xy plane at the point

    The two normal vectors for the planes are <1, -2, 1> and <2, 1, 1>. The cross product of the two vectors will give a vector that is parallel to the line of intersection:

    Thus, the symmetric equations for the line of intersection are:

    (b) the angle of intersection between the two planes can be found using the equation:

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 7:35 pm ad1c9bdddf>
    https://brainmass.com/math/symmetric-equations-line-intersection-201051

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