What is this ?

Asked by alanpeter9611 | 14th Feb, 2019, 05:05: PM

Expert Answer:


Equation of PQ with direction ratios  (2, -1, 1) is
begin mathsize 12px style R with rightwards arrow on top space equals space open parentheses i with hat on top space plus 3 space j with hat on top space plus space 4 k with hat on top close parentheses space plus space lambda space open parentheses 2 i with hat on top space minus space j with hat on top space plus space k with hat on top close parentheses
space equals space open parentheses 1 plus 2 lambda close parentheses space i with hat on top space plus space open parentheses 3 minus lambda close parentheses j with hat on top space plus space open parentheses 4 plus lambda close parentheses space k with hat on top space
I f space t h e space c o e f f i c i e n t s space o f space c o m p o n e n t space v e c t o r space a r e space c o o r d i n a t e space p o i n t s space o f space Q comma space t h e n space
2 open parentheses 1 plus 2 lambda close parentheses space minus space 1 open parentheses 3 minus lambda close parentheses space plus space 2 open parentheses 4 plus lambda close parentheses space plus space 3 space equals 0
t h e n space lambda space equals space minus 1
c o r r d i n a t e s space o f space Q space a r e space equals space left parenthesis space 1 plus 2 lambda space comma space 3 minus lambda comma space 4 plus lambda space right parenthesis space equals space left parenthesis negative 1 comma space 4 comma space 3 space right parenthesis
i f space P apostrophe left parenthesis x comma y comma z right parenthesis space i s space i m a g e space o f space P space left parenthesis 1 comma 3 comma 4 right parenthesis space space t h e n space Q space i s space m i d space p o i n t. space space H e n c e

left parenthesis x plus 1 right parenthesis divided by 2 space equals space minus 1 space space comma space space left parenthesis y plus 3 right parenthesis divided by 2 space equals space 4 comma space space t h e n space left parenthesis z plus 4 right parenthesis divided by 2 space equals 3

c o o r d i n a t e s space o f space P apostrophe space equals space left parenthesis negative 3 comma space 5 comma space 2 right parenthesis

d i s tan c e space b e t w e e n space P space a n d space P apostrophe space equals space square root of open parentheses 1 plus 3 close parentheses squared plus open parentheses 3 minus 5 close parentheses squared plus open parentheses 4 minus 2 close parentheses squared end root space equals space 2 square root of 6 end style

Answered by Thiyagarajan K | 15th Feb, 2019, 11:32: AM

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