Question

given that vector OA = 4i+3j and C is a point on OA such that the magnitude of vector OC is 16/5.
a/ find vector OC.
b/ is vector OB = i+4j, show that BC is perpendicular to OA.

Answer 1

a) since C is on OA so it's directiion is same as OA so only magnitude is changing
so OC=(OA/|OA|)*(16/5)=(64/25)i+(48/25)j
b) given B(1,4) & C((64/25),(48/25))
so BC=((64/25)-1)i+((48/25)-4)j=(39/25)i-(52/25)j
now if BC.OA=0 then we can say that OA and BC are perpendicular
BC.OA=(156/25)-(156/25)=0
hence proved