Relative to the origin O, the position vector of A is 6i+6j and the position vector of B is 12i−2j. The point C lies on vec(AB) such that vec(AC)=3/4 vec(AB). Find the position vector of C

Medenovgj 2022-09-27 Answered
How to find a position vector given several other position vectors with a given relationship?
Relative to the origin O , the position vector of A is 6 i + 6 j and the position vector of B is 12 i 2 j. The point C lies on A B − such that A C = 3 4 A B . Find the position vector of C.
As of now, I have found A B and A C :
A B = O B O A
A B = 12 i 2 j ( 6 i + 6 j )
A B = 12 i 2 j 6 i 6 j
A B = 6 i 8 j
A C = 3 4 A B
A C = 3 4 ( 6 i 8 j )
A C = 3 4 2 ( 3 i 4 j )
A C = 3 2 ( 3 i 4 j )
A C = 3 ( 3 i 4 j ) 2
A C = 9 i 12 j 2
How would O C be found?
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Answers (1)

Laylah Bean
Answered 2022-09-28 Author has 4 answers
You know A B = O B O A
Similarly A C = O C O A O C = O A + A C = ( 6 i ^ + 6 j ^ ) + ( 4.5 i ^ 6 j ^ ) = 10.5 i ^
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