Let i - j +2 k and i +2 j -2 k be the position vectors of points A and B respectively. If C is a point on the line joining A and B such that BC =10 , then the position vector of C can be

Step-by-step solution

OA = i - j +2 k , OB = i +2 j -2 k aligned & OC = OA +t( OB - OA )=( i - j +2 k )+ t (3 j -4 k ) & OC = i +(3 t -1) j +(2-4 t ) k & | BC |=10 & | OC - OB |=10 aligned aligned & |0 i +(3 t-1-2) j +(2-4 t+2) k |=10 & (3 t-3)^2+(4-4 t)^2=100 & 9(t-1)^2+16(t-1)^2=100 & 25(t-1)^2=100 (t-1)^2=4 & t-1=2 t=3 & O C = i +8 j -10 k aligned