The point if intersection of the lines l₁: r (t)=( i -6 j +2 k )+t( i +2 j + k )l₂: R (u)=(4 j + k )+u(2 i + j +2 k ) is

Step-by-step solution

Put r =x i +y j +z k x i +y j +z k =( i -6 j +2 k )+t( i +2 j + k ) Any point on line is P(1+t,-6+2 t, 2+t) is satisfied the second equation of line. aligned & (1+t) i +(-6+2 t) j +(2+t) k & =2 u i +(4+u) j +(1+2 u) k aligned On equating the coefficients of i , j and k , we get 1+t=2 u aligned & t-2 u+1=0 & -6+2 t=4+u & 2 t-u-10=0 & and 2+t=1+2 u & t-2 u+1=0 & aligned On solving Eqs. (i) and (ii), we get gathered t=7, u=4 P(1+7,-6+2 7,2+7)=P(8,8,9) gathered