If the line joining the points i + j and 3 i + j - k meets the plane that passes through the point 2 i +4 j and parallel to the vectors 3 j +5 k and 3 i - k at, P , then the position vector of the point P is

Step-by-step solution

Equation of line joining points ( i + j ) and (3 i + j - k ) in cartesian form is x-1 2 = y-1 0 = z -1 =r( let ) Then, point on line Eq. (i) is p(2 r+1,1,-r) . Now, equation of plane passes through the point (2 i +4 j ) and parallel to the vectors (3 j +5 k ) and (3 i - k ) in cartesian form is aligned & | array ccc x-2 & y-4 & z 0 & 3 & 5 3 & 0 & -1 array | & =0 & -3(x-2)+15(y-4)-9 z & =0 & 3 x-15 y+9 z+54 & =0 aligned Let the point P(2 r+1,1,-r) on the plane Eq. (ii) itself, so r=14 So, position vector of the poi