KCET2018MathematicsThree Dimensional Geometry
The image of the point ( (1,6,3) ) in the line ( x 1 = y-1 2 = z-2 3 ) is
Options
- A( (1,0,7) )
- B( (7,0,1) )
- C( (2,7,0) )
- D((-1,-6,-3) )
Correct answer
A. ( (1,0,7) )
Step-by-step solution
Given line [ x 1 = y-1 2 = z-2 3 (1) ] Point ( P(1,6,3) ) and reflection ( Q ). Let ( x 1 = y-1 2 = z-2 3 = ) and point ( R ) on line. So, coordinates of ( R ) is ( ( , 1+2 , 2+3 ) ) Direction ratios of line is ( (1,2,3) ). Since PR is perpendicular to the given line. Then, direction ratios of ( P R =( -1,2 -5,3 -1) ) So, ( -1+2(2 -5)+3(3 -1)=0 ) ( 14 =14 =1 ) Therefore, ( R(1,3,5) ) and ( Q(1,0,7) )