# SOLUTION: find the distance from point Q to line l (matriks) Q=(0, 1, 0) l= [x y z] = [1 1 1] + t[-2 0 3]

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 Question 54307This question is from textbook Linear Algebra : find the distance from point Q to line l (matriks) Q=(0, 1, 0) l= [x y z] = [1 1 1] + t[-2 0 3]This question is from textbook Linear Algebra Answer by Edwin McCravy(8999)   (Show Source): You can put this solution on YOUR website!```find the distance from point Q to line l (matrix) Q=(0, 1, 0) line = < x y z > = < 1 1 1 > + t< -2 0 3 > Formula: __ ||PQ × u|| D = ------------ ||u|| where u is the direction vector for the line and P is a point on the line Using the direction numbers -2, 0, and 4, you know that the direction vector for the line is u = < -2, 0, 4 > To find a point on the line, let t = 0 and obtain P = (1, 1, 1) Thus, since Q = (0, 1, 0) __ PQ = < 0-1, 1-1, 0-1 > = < -1,0,-1 > __ Now get the cross product PQ × u __ | i j k| PQ × u = |-1 0 -1| = i(0+0) - j(-4-2) + k(0+0) = -6j |-2 0 4| __ ||PQ × u|| = ||-6j|| = 6 ____________ ______ __ _ ||u|| = Ö(-2)²+0²+ 4² = Ö4+0+16 = Ö20 = 2Ö5 __ _ ||PQ × u|| 6 3 3Ö5 D = ------------ = ----- = ---- = ----- ||u|| 2Ö5 Ö5 5 Edwin```