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Parametric vector form of the line 
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#1
Apr2812, 08:49 PM

P: 34

The parametric vector form of the line 1
is given as r1 = u1 + rv1 (r element of real field) where u1 is the position vector of P1 = (1,1,−3) and v1=vectorP1P2 where P2 = (3,3,−2) . The parametric vector form of the line 2 is given as r2 = u2 + sv2 (s element of real field) where 2 u is the position vector of P3 = (−2,0,2) and v2= −j− k . (a) Give the parametric scalar equations of the lines l1 and l2 . (b) Find the unit vector ˆn with negative i component which is perpendicular to both l1 and l2 (c) The shortest distance between two lines is the length of a vector that connects the two lines and is perpendicular to both lines. For l1 and l2 this is expressed in the vector equation 2 1 r −r = tnˆ where t element of real field is a parameter. Write this equation as 3 scalar equations and hence obtain a system of three linear equations for the three parameters r, s and t . (d) Solve this system of equations for r, s and t and hence find the shortest distance between the two lines 1 and 2 . (e) Find the point Q on line 1 which is closest to line 2 I've done bits and pieces of the question bu i'm especially stuck on parts c d and e. please help thank you 


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