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8 March, 18:50

Find a vector parallel to the line of intersection of the planes given by 2x + z = 5 and x + y - z = 4

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  1. 8 March, 21:46
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    The normal to the given plane P1: 2x+z=5 is N1=, and similarly

    the normal to the given plane P2: x+y-z=4 is N2=, and similarly

    The normal to the above normals is parallel to the intersection of planes P1 and P2, which is given by the cross product of N1 and N2:

    V = N1 x N2 =

    i j k

    2 0 1

    1 1 - 1

    = V

    =V

    A vector parallel to the intersection of P1 and P2 is V.

    Check:

    substitute V in P1: 2 (-1) + 0 + (2) = 0 = > V is parallel to P1.

    substitute V in P2: (-1) + (3) - (2) = 0 = > V is parallel to P2

    Therefore V is parallel to intersection of P1 and P2.
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