a) Given the line in vector form r = < 2,1,-3> +t < -1,2,-3>, determine if...

 

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a) Given the line in vector form r = < 2,1,-3> +t < -1,2,-3>, determine if the following points are on the line or not: 1. (3,0,2) II. (10,-25,39) b) Determine the parametric equation of a line that passes through the points P(2,1,-3) and Q(7,1,6). c) Determine the standard equation of a plane that intersects and is orthogonal to T= <2,1,-3> +t < -1,2,-3>. d) Determine the intersection of the planes I: 3x-2y+4z = 20 and 2:x-2y-3z=0. e) Determine the exact value of the point of intersection between r= <2,1,-3> +t < -1,2,-3> and I: 3x-2y+4z = 20. Check that the intersection is correct by substituting it into the appropriate equation. f) Prove that the following lines are skew lines and determine the shortest distance between them. Ensure that you provide a quality sketch which labels all key information from the question. x=-4+2t x=4+2T Ly 5-t and L: y=T z=6-3t z=6+3r a) Given the line in vector form r = < 2,1,-3> +t < -1,2,-3>, determine if the following points are on the line or not: 1. (3,0,2) II. (10,-25,39) b) Determine the parametric equation of a line that passes through the points P(2,1,-3) and Q(7,1,6). c) Determine the standard equation of a plane that intersects and is orthogonal to T= <2,1,-3> +t < -1,2,-3>. d) Determine the intersection of the planes I: 3x-2y+4z = 20 and 2:x-2y-3z=0. e) Determine the exact value of the point of intersection between r= <2,1,-3> +t < -1,2,-3> and I: 3x-2y+4z = 20. Check that the intersection is correct by substituting it into the appropriate equation. f) Prove that the following lines are skew lines and determine the shortest distance between them. Ensure that you provide a quality sketch which labels all key information from the question. x=-4+2t x=4+2T Ly 5-t and L: y=T z=6-3t z=6+3r