1. [10] Let be the line in 3-space that passes through the points A = (3,1,...

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1. [10] Let be the line in 3-space that passes through the points A = (3,−1, 2) and B = (5,4,-1). (a) Find a set of parametric equations for l. (b) Determine the set of all points on whose distance from A is at most half the distance from A to B. (c) Determine the value of k for which the point C = (k, k-1, k- 6) lies on l. (d) Determine the unique point D at which intersects the plane with scalar equation -2x1 + x2x3 = 3. 2. [10] Let' be the line in 3-space that passes through the point (1,−1, 1) and is parallel to the line from Problem 1 above. (a) Find a set of parametric equations for the plane P in 3-space that passes through the origin and contains the line l'. (b) Find a vector equation for the line of intersection of the plane P from part (a) and the plane P' with scalar equation x₁ + x₂ + x3 = 0. 1. [10] Let be the line in 3-space that passes through the points A = (3,−1, 2) and B = (5,4,-1). (a) Find a set of parametric equations for l. (b) Determine the set of all points on whose distance from A is at most half the distance from A to B. (c) Determine the value of k for which the point C = (k, k-1, k- 6) lies on l. (d) Determine the unique point D at which intersects the plane with scalar equation -2x1 + x2x3 = 3. 2. [10] Let' be the line in 3-space that passes through the point (1,−1, 1) and is parallel to the line from Problem 1 above. (a) Find a set of parametric equations for the plane P in 3-space that passes through the origin and contains the line l'. (b) Find a vector equation for the line of intersection of the plane P from part (a) and the plane P' with scalar equation x₁ + x₂ + x3 = 0.

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1 a The parametric equations for l is given by lt 3 1 2 t2 5 3 b The set of all points on l whose di... View the full answer