SOLUTION: A and B have position vectors 3i + 6j and 6i +3j respectively. C lies on OA where OC : CA = 1:2 and D lies on OB where OD : DB = 2:1. (i) Find the position vectors of C and D (ii)F

Algebra ->  Vectors -> SOLUTION: A and B have position vectors 3i + 6j and 6i +3j respectively. C lies on OA where OC : CA = 1:2 and D lies on OB where OD : DB = 2:1. (i) Find the position vectors of C and D (ii)F      Log On


   

Question 1196159: A and B have position vectors 3i + 6j and 6i +3j respectively. C lies on OA where OC : CA = 1:2 and D lies on OB where OD : DB = 2:1. (i) Find the position vectors of C and D (ii)Find vector CD and vector AB in terms
Answer by greenestamps(13203) About Me  (Show Source):
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OC:CA = 1:2 means vector OC is 1/(1+2) = 1/3 of vector OA.

OC = (1/3)(3i+6j) = i+2j

The position vector of C is i+2j

OD:DB = 2:1 means vector OD is 2/(2+1) = 2/3 of vector OB.

OD = (2/3)(6i+3j) = 4i+2j

The position vector of D is 4i+2j

Vector CD is vector OD minus vector OC.

CD = (4i+2j)-(i+2j) = 3i

Vector AB is vector OB minus vector OA.

AB = (6i+3j)-(3i+6j) = 3i-3j