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08%20-%20Line%20in%20Space

# 08%20-%20Line%20in%20Space - PROBLEMS(1 08 LINE IN SPACE...

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PROBLEMS 08 - LINE IN SPACE Page 1 ( 1 ) Obtain the equations of the line through A ( 1, 2, 1 ) and B ( 2, 3, - 1 ) in vector and Cartesian forms. = = + = 2 1 z 1 2 y 1 1 x R, k ), 2 r : Ans 1, 1, ( k ) 1 2, 1, ( - - - - - ( 2 ) Find the angle between 2 1 z 5 3 y 2 1 x - - - + = = and 3 3 z 1 1 y 2 1 x + + = = - . 154 3 cos : Ans 1 - ( 3 ) Prove that the lines r = ( 1, 2, 6 ) + k ( 1, 3, 5 ), k R and r = ( - 1, 3, 5 ) + k ( 2, 1, 1 ), k R are non-coplanar. ( 4 ) Obtain the perpendicular distance of the line r = ( 2, 1, 5 ) + k ( 1, 0, 1 ), k R from P ( 1, 2, 1 ). 2 11 : Ans ( 5 ) Show that 5 2 z 3 1 y 2 1 x - - - = = + and 1 1 z 2 1 y 3 x - - = = are skew lines. Find the shortest distance between the. 3 2 : Ans ( 6 ) Obtain the co-ordinates of the foot of perpendicular from ( 2, 4, - 1 ) on r = ( - 5, - 3, 6 ) + k ( 1, 4, - 9 ), k R and find the distance of the point from the line. [ Ans: ( - 4, 1, - 3 ), 7 ] ( 7 ) Obtain the vector and Cartesian forms of equations of the line through A ( 1, 2, 3 ) in the direction ( - 1, 1, 2 ) and find the co-ordinates of the points on the line at a distance 6 from A.

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08%20-%20Line%20in%20Space - PROBLEMS(1 08 LINE IN SPACE...

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