lp - N . If two planes are perpendicular then they their...

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Line Info Sheet r = r 0 + t v ( x, y, z ) = ( x 0 , y 0 , z 0 ) + t ( a, b, c ) x = x 0 + at y = y 0 + bt z = z 0 + ct x - x 0 a = y - y 0 b = z - z 0 c If two lines are parallel then they have the same direction vectors v . If two lines are perpendicular then their direction vectors v 1 , v 2 satisfy the equation v 1 · v 2 = 0. If two lines in the plane are perpendicular then if one has direction vector v 1 = ( a, b ), the other one has direction vector which you can take to be v 2 ( b, - a ). If the lines are not in 2D, then you can’t say much more than v 1 · v 2 = 0. If two points P, P 0 both lie on a line then P 0 P has same direction vector v as the line, so you can take P 0 P = v . Planes N · ( r - r 0 ) = 0 ( a, b, c i · ( x - x 0 , y - y 0 , z - z 0 i = 0 a ( x - x 0 ) + b ( y - y 0 ) + c ( z - z 0 ) = 0 If two planes are parallel then they have the same normal vectors
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Unformatted text preview: N . If two planes are perpendicular then they their direction vectors N 1 , N 2 satisfy the equation N 1 N 2 = 0, and theres not much more that you can say. If two vectors A , B both are parallel to a plane then A B has same direction vector N as the plane, so you can take A B = N . If two points P, P both lie on a plane then P P is parallel to the plane. You can say that N P P = 0 If a line with direction A is perpendicular to a plane then N and A are parallel vectors. You can say that N = A ....
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