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T h e space r a t i o space i n space w h i c h space t h e space l i n e space s e g m e n t space j o i n i n g space t h e space p o i n t s space left parenthesis 1 comma 2 comma 3 right parenthesis space a n d space left parenthesis 4 comma 5 comma 6 right parenthesis
i s space d i v i d e d space b y space t h e space p l a n e space x plus y plus z equals 1 space i s ?

Please provide solution to this question

Asked by Topperlearning User 16th November 2016, 12:54 AM
Answered by Expert
Answer:

L e t space P space b e space t h e space p o i n t space w h i c h space d i v i d e s space t h e space l i n e space s e g m e n t space i n space t h e space r a t i o space k colon 1 space
a n d space P space a l s o space l i e s space o n space t h e space g i v e n space p l a n e.
c o o r d i n a t e s space o f space P space a r e
x equals fraction numerator 4 k plus 1 over denominator k plus 1 end fraction
y equals fraction numerator 5 k plus 2 over denominator k plus 1 end fraction
z equals fraction numerator 6 k plus 3 over denominator k plus 1 end fraction
P space l i e s space o n space t h e space p l a n e space s o
fraction numerator 4 k plus 1 over denominator k plus 1 end fraction plus fraction numerator 5 k plus 2 over denominator k plus 1 end fraction plus fraction numerator 6 k plus 3 over denominator k plus 1 end fraction equals 1
rightwards double arrow 15 k plus 6 equals k plus 1
rightwards double arrow 14 k equals negative 5
rightwards double arrow k equals negative 5 over 14
S o space t h e space p l a n e space d i v i d e s space t h e space l i n e space s e g m e n t space e x t e r n a l l y space i n space t h e space r a t i o space 5 colon 14

Answered by Expert 16th November 2016, 2:54 AM
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