CBSE Class 12-science Answered

If the point R(4,y,z) lies on the line segment PQ, where P(2,-3,4) and Q(8,0,10), then the distance between R and the origin is: A. 2*(14)^1/2 B. 9 C. 2*(21)^1/2 D. (53)^1/2

Asked by bjayanta | 14 Apr, 2019, 12:01: PM

Expert Answer

G i v e n colon space P left parenthesis 2 comma negative 3 comma 4 right parenthesis space a n d space Q left parenthesis 8 comma 0 comma 10 right parenthesis D i r e c t i o n space v e c t o r space equals space d equals stack P Q with rightwards arrow on top equals left parenthesis 6 comma 3 comma 6 right parenthesis N o w comma space e q u a t i o n space o f space l i n e space p a s sin g space t h r o u g h space P Q thin space i s space g i v e n space b y colon fraction numerator x minus 2 over denominator 6 end fraction equals fraction numerator y plus 3 over denominator 3 end fraction equals fraction numerator z minus 4 over denominator 6 end fraction space......... space left parenthesis i right parenthesis S i n c e comma space R thin space l i e s space o n space t h e space l i n e space P Q space s o space i t space s a t i s f i e s space t h e space e q u a t i o n space i f space l i n e space P Q L e t space fraction numerator x minus 2 over denominator 6 end fraction equals fraction numerator y plus 3 over denominator 3 end fraction equals fraction numerator z minus 4 over denominator 6 end fraction equals t rightwards double arrow x equals 6 t plus 2 comma space y equals 3 t minus 3 comma space z equals 6 t plus 4 A n y space p o i n t space o n space t h e space l i n e space left parenthesis i right parenthesis space h a s space c o o r d i n a t e s space i n space t h e space f o r m space left parenthesis 6 t plus 2 comma space 3 t minus 3 comma space 6 t plus 4 right parenthesis S i n c e space R space l i e s space o n space left parenthesis i right parenthesis comma space s o space c o o r d i n a t e s space o f space R space w i l l space b e space o f space t h e space f o r m space left parenthesis 6 t plus 2 comma space 3 t minus 3 comma space 6 t plus 4 right parenthesis B u t space R space i s space g i v e n space a s space left parenthesis 4 comma space y comma z right parenthesis rightwards double arrow 6 t plus 2 equals 4 rightwards double arrow t equals 1 third T h u s comma space c o o r d i n a t e s space o f space R space a r e space open parentheses 4 comma negative 2 comma 6 close parentheses N o w comma space d i s tan c e space b e t w e e n space R space a n d space o r i g i n thin space O left parenthesis 0 comma 0 comma 0 right parenthesis space i s equals square root of left parenthesis 4 minus 0 right parenthesis squared plus left parenthesis negative 2 minus 0 right parenthesis squared plus left parenthesis 6 minus 0 right parenthesis squared end root equals square root of 16 plus 4 plus 36 end root equals square root of 56 equals 2 square root of 14

Answered by Renu Varma | 15 Apr, 2019, 02:40: PM

CBSE Class 12-science Answered

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CBSE Class 12-science Answered

Application Videos

ProblemsbasedonIntoFunction-I

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Concept Videos

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Graphical representation of inverse trigonometric funct ...

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