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CBSE Class 11-science Answered

find the co ordinates of points which trisect the line segment joing the points p(4,2,-6)andq(10,-16,6).
sir please briefly explain it and kindly dont refer that to see ncert solutions.....thank you
Asked by Masood khan | 16 Feb, 2016, 07:00: PM
answered-by-expert Expert Answer
Let space straight A left parenthesis straight x subscript 1 comma space straight y subscript 1 space comma straight z subscript 1 space right parenthesis space space and space straight B left parenthesis straight x subscript 2 comma space straight y subscript 2 space comma straight z subscript 2 space right parenthesis space be space the space two space points space trisecting space the space line space segment space joining space the space points space straight P left parenthesis 4 comma space 2 comma space minus 6 right parenthesis space and space straight Q left parenthesis 10 comma space minus 16 comma space 6 right parenthesis. Therefore space straight A space divides space the space space the space line space segment space joining space the space points space straight P left parenthesis 4 comma space 2 comma space minus 6 right parenthesis space and space straight Q left parenthesis 10 comma space minus 16 comma space 6 right parenthesis space in space the space ration space 1 colon 2. straight B space divides space the space space the space line space segment space joining space the space points space straight P left parenthesis 4 comma space 2 comma space minus 6 right parenthesis space and space straight Q left parenthesis 10 comma space minus 16 comma space 6 right parenthesis space in space the space ration space 2 colon 1. By space section space formula space we space can space write straight A left parenthesis straight x subscript 1 comma space straight y subscript 1 space comma straight z subscript 1 space right parenthesis space equals open square brackets fraction numerator 2 cross times 4 plus 1 cross times 10 over denominator 2 plus 1 end fraction comma fraction numerator 2 cross times 2 plus 1 cross times left parenthesis negative 16 right parenthesis over denominator 2 plus 1 end fraction comma fraction numerator 2 cross times left parenthesis negative 6 right parenthesis plus 1 cross times 6 over denominator 2 plus 1 end fraction close square brackets equals open parentheses 6 comma space minus 4 comma space minus 2 close parentheses straight B left parenthesis straight x subscript 1 comma space straight y subscript 1 space comma straight z subscript 1 space right parenthesis space equals open square brackets fraction numerator 1 cross times 4 plus 2 cross times 10 over denominator 1 plus 2 end fraction comma fraction numerator 1 cross times 2 plus 2 cross times left parenthesis negative 16 right parenthesis over denominator 1 plus 2 end fraction comma fraction numerator 1 cross times left parenthesis negative 6 right parenthesis plus 2 cross times 6 over denominator 1 plus 2 end fraction close square brackets equals open parentheses 8 comma space minus 10 comma space 2 close parentheses The space points space open parentheses 6 comma space minus 4 comma space minus 2 close parentheses space and space open parentheses 8 comma space minus 10 comma space 2 close parentheses space trisect space the space line space segment space joining space the space points space straight P left parenthesis 4 comma space 2 comma space minus 6 right parenthesis space and space straight Q left parenthesis 10 comma space minus 16 comma space 6 right parenthesis.
Answered by Vijaykumar Wani | 17 Feb, 2016, 10:56: AM

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