Question

show that line joining points (6,-4,4),(0,0,-4)and intersecting line joining points (-1,-2,-3),(-1,2,-5)

Answer 1

SOLUTION

TO PROVE

The line joining points (6 , - 4 , 4 ) , (0 , 0 , - 4 ) and intersecting line joining points ( - 1 , - 2 , - 3 ) ,( 1 , 2 , - 5 )

EVALUATION

Let the given points are A(6 , - 4 , 4 ) , B(0 , 0 , - 4 ) , C( - 1 , - 2 , - 3 ) , D( 1 , 2 , - 5 )

Here the mid point of the line joining the points C and D

= Mid point of the line CD

$\displaystyle \sf{ = \bigg( \frac{ - 1 + 1}{2}, \frac{ - 2 + 2}{2} , \frac{ - 3 - 5}{2} \bigg)}$

$\displaystyle \sf{ = \bigg( \frac{ 0}{2}, \frac{ 0}{2} , \frac{ - 8}{2} \bigg)}$

$\displaystyle \sf{ = ( 0, 0 , - 4 )}$

Mid point of the line CD is the point B

Hence the line CD intersects the line AB at the point B

Hence line joining points (6 , - 4 , 4 ) , (0 , 0 , - 4 ) and intersecting line joining points ( - 1 , - 2 , - 3 ) ,( 1 , 2 , - 5 )

Hence proved

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