(4) Consider the line segment that starts at the point P = (3, 2, 7) and ends at the point Q=(5,-1,5). In this problem y

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4 Consider The Line Segment That Starts At The Point P 3 2 7 And Ends At The Point Q 5 1 5 In This Problem Y 1 (64.67 KiB) Viewed 60 times

Please help with all parts thank you will upvote
(4) Consider the line segment that starts at the point P = (3, 2, 7) and ends at the point Q=(5,-1,5). In this problem you will find the distance between this line segment and the plane containing the point (0, 0, 0) with normal vector Ñ= (1, 1, -1). (a) Find an equation for the (infinite) line (t) that contains the points (3, 2, 7) and (5,-1,5). What values of t correspond to the line segment between those two points? (b) Find an equation for the plane containing the point (0, 0, 0) with normal vector N = (1, 1,-1). (c) Show that the line segment PQ does not intersect the plane. Hint: the line from (a) does intersect the plane from (b). One approach is to show that this intersection point does not lie on the line segment. (d) For part (d), you may assume that the line segment does not intersect the plane. Find the distance between the line segment PQ and the plane. Justify your approach.