 Hi and welcome to the session. This is the body question. The question says, find the coordinates of the foot of the propellicular drawn from the point A having coordinates 1, 8, 4 to the line joining the points B having coordinates 0, minus 1, 3 and C having coordinates 2, minus 3, minus 5. So this is the propellicular to the line B, C and we have to find coordinates of M. Let's now begin with the solution. We will first find direction ratios of the line joining the points B and C. The direction ratios of line joining having coordinates 0, minus 1, 3 and C having coordinates 2, minus 3, minus 1, R 2, minus 0, minus 3, plus 1, minus 1, minus 3, that is 2, minus 2, minus 4. Now vector along the line B, C let us denote by vector B, minus 2 j cap, minus 4 k cap. Position vector point B having coordinates 0, minus 1, 3 on the line is 0 i cap, minus j cap, plus 3 k cap. And let us denote this vector by vector A. Equation of line S, vector R equals to vector A plus lambda times vector B. Vector A is equal to 0 i cap, minus j cap, plus 3 k cap and vector V is equal to 2 i cap, minus 2 j cap, minus 4 k cap. Appendicular B, C, therefore position vector of M will be 0 plus 2 lambda i cap, plus minus 1 minus 2 lambda j cap, plus 3 minus 4 lambda k cap. The A M is equal to position vector of minus position vector of A. Position vector of M is i cap, plus minus 1 minus 2 lambda j cap, plus 3 minus 4 lambda k cap. Position vector of A is plus 4 k cap. Now this is equal to 2 lambda minus 1 i cap, plus 2 lambda j cap, plus minus 1 minus 4 lambda k cap. Since vector A M is equal to vector B C, therefore we have denoted vector along B C by vector B. So we have vector A M dot vector V equals to 0. This implies vector A M plus minus 1 minus 4 lambda k cap, minus 2 lambda into minus 2 minus 1 minus 4 lambda into minus 4 is equal to 0. Now this implies 4 lambda minus 2 plus 18 plus 4 lambda plus 4 plus 16 lambda is equal to 0. This implies 24 lambda plus 20 is equal to 0. And this implies lambda is equal to minus 5 by 6. And let's name this equation as equation 1. So now we will quote minus 5 by 6 in 1. Minus 5 by 6 we have 0 plus 2 into minus 5 by 6 plus minus 1 minus 2 into minus 5 by 6 k cap minus 5 by 6. Here we will have j cap and here we will have k cap. This is equal to plus 1 plus 5 by 3 k cap.