let vector OP = 2i + 3j and vector OQ = -6i+4j. R is a point on vector PQ such that PR/RQ = k/1, where k0.
a/ express vector OR in terms of k, i and j.
b/ express (vector OP)dot(vector OR) and (vector OQ)dot(vector OR) in terms of k.
c/ Find the value of k such that OR bisects angle POQ.

Question

let vector OP = 2i + 3j and vector OQ = -6i+4j. R is a point on vector PQ such that PR/RQ = k/1, where k>0.
a/ express vector OR in terms of k, i and j.
b/ express (vector OP)dot(vector OR) and (vector OQ)dot(vector OR) in terms of k.
c/ Find the value of k such that OR bisects angle POQ.

calvin · Answer

a/vectorOR=[(4k+3)/(k+1)]i+[(2-6k)/(k+1)]j
b/(vectorOP)dot(vectorOR)=(12-10k)/(k+1);(vector OQ)dot(vector OR)=-(48k+10)/(k+1)
c/k=1

calvin · Answer

correction:c/k=7/34