CBSE Class 12-science Answered

Find the image of the point (1,3,4) on the plane 2x-y+z+3=0.

Asked by Navya Benny | 22 Dec, 2015, 01:27: PM

Expert Answer

L e t space P left parenthesis 1 comma 3 comma 4 right parenthesis space b e space a space p o i n t L e t space M space b e space t h e space p o i n t space o n space t h e space p l a n e. E q u a t i o n space o f space t h e space p l a n e space i s space 2 x minus y plus z plus 3 equals 0 T h u s space t h e space e q u a t i o n space o f space t h e space p l a n e space i s colon fraction numerator x minus 1 over denominator 2 end fraction equals fraction numerator y minus 3 over denominator negative 1 end fraction equals fraction numerator z minus 4 over denominator 1 end fraction equals k A n y space p o i n t space o n space t h e space a b o v e space l i n e comma space P M space i s space o f space t h e space f o r m comma x equals 2 k plus 1 semicolon space y equals negative k plus 3 semicolon space z equals k plus 4 S u b s t i t u t i n g space t h e space a b o v e space v a l u e s space i n space t h e space e q u a t i o n space o f space t h e space p l a n e space w e space h a v e comma space 2 open parentheses 2 k plus 1 close parentheses minus open parentheses negative k plus 3 close parentheses plus open parentheses k plus 4 close parentheses plus 3 equals 0 rightwards double arrow 4 k plus 2 plus k minus 3 plus k plus 4 plus 3 equals 0 rightwards double arrow 6 k plus 6 equals 0 rightwards double arrow k equals negative 1 T h u s space t h e space c o o r d i n a t e s space o f space M space a r e colon x equals 2 open parentheses negative 1 close parentheses plus 1 equals negative 1 y equals negative open parentheses negative 1 close parentheses plus 3 equals 4 z equals open parentheses negative 1 close parentheses plus 4 equals 3 L e t space Q open parentheses x apostrophe comma y apostrophe z apostrophe close parentheses space b e space t h e space i m a g e space o f space P. T h u s comma space M space i s space t h e space m i d p o i n t space o f space P Q. T h e r e f o r e comma minus 1 equals fraction numerator 1 plus x apostrophe over denominator 2 end fraction semicolon space 4 equals fraction numerator 3 plus y apostrophe over denominator 2 end fraction semicolon space 3 equals fraction numerator 4 plus z apostrophe over denominator 2 end fraction rightwards double arrow x apostrophe equals negative 3 semicolon space y apostrophe equals 5 semicolon space z apostrophe equals 2

Answered by Vimala Ramamurthy | 22 Dec, 2015, 05:13: PM

CBSE Class 12-science Answered

Concept Videos

Cartesian equation of a line

Skew Lines

Equation of a Plane

Intercept Form and Family of Planes

Co-planarity of two lines

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CBSE Class 12-science Answered

Concept Videos

Cartesian equation of a line

Skew Lines

Equation of a Plane

Intercept Form and Family of Planes

Co-planarity of two lines

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