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If $A (1, 2, 3), B (2, 3, 4)$ and $A B$ is produced up to $C$ such that $2 A B = B C$ , then $C =$

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(5,4,6)

(4,1,4)

52,72,92

(4,5,6)

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detailed solution

Correct option is D

Given 2AB=BCit gives AB¯=BC¯ 2(OB¯−OA¯)=(OC¯−OB¯)2OB¯−2OA¯+OB¯=OC¯OC¯=3OB¯−2OA¯It implies OC¯=3(2i+3j+4k)−2(i+2j+3k)=6i+9i+12k−2i−4j−6k=4i+5j+6kTherefore, C(4,5,6)

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If A(1,2,3),B(2,3,4)and AB is produced up to Csuch that 2AB=BC, then C=

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If $A (1, 2, 3), B (2, 3, 4)$ and $A B$ is produced up to $C$ such that $2 A B = B C$ , then $C =$