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Question: The point dividing the line joining the points \(( 1,2,3 )\)and \(( 3 , - 5,6 )\) in the ratio \(3 :...

The point dividing the line joining the points (1,2,3)( 1,2,3 )and (3,−5,6)( 3 , - 5,6 ) in the ratio 3:−53 : - 5 is

A

(2,−252,32)\left( 2 , \frac { - 25 } { 2 } , \frac { 3 } { 2 } \right)

B

(−2,252,−32)\left( - 2 , \frac { 25 } { 2 } , \frac { - 3 } { 2 } \right)

C

(2,252,32)\left( 2 , \frac { 25 } { 2 } , \frac { 3 } { 2 } \right)

D

None of these

Answer

(−2,252,−32)\left( - 2 , \frac { 25 } { 2 } , \frac { - 3 } { 2 } \right)

Explanation

Solution

x=−5+9−2=−2,y=−5(2)+3(−5)−2=252x = \frac { - 5 + 9 } { - 2 } = - 2 , y = \frac { - 5 ( 2 ) + 3 ( - 5 ) } { - 2 } = \frac { 25 } { 2 }

z=−5(3)+3(6)−2=−32z = \frac { - 5 ( 3 ) + 3 ( 6 ) } { - 2 } = - \frac { 3 } { 2 }.