 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that find the value of x such that the line through A with coordinates 5, 4, minus 2 and B with coordinates 3, x, minus 6 is parallel to line through C with coordinates minus 2, 8, minus 3 and B with coordinates 2, 2, 5. We know that two lines are parallel if A1 upon A2 is equal to B1 upon B2 is equal to C1 upon C2 where A1, B1, C1 and A2, B2, C2 are the direction ratios of the two lines. With this key idea let us proceed with the solution. Here we need to find the value of x such that line AB is parallel to line 3D. So first of all we shall find direction ratios of line AB and CD. Here coordinates of AR 5, 4, minus 2 and coordinates of BR 3, x, minus 6 and we know that direction ratios of any line say PQ is given by x2 minus x1, y2 minus y1, z2 minus z1 where x1, y1, z1 and x2, y2, z2 are the coordinates of point P and Q respectively. Therefore direction ratios of line AB are given by x2 minus x1 that is 3 minus 5, y2 minus y1 that is x minus 4 and z2 minus z1 that is minus 6 minus of minus 2 which is equal to minus 2 x minus 4 minus 4. Also coordinates of point CR minus 2, 8, minus 3 and coordinates of point DR 2, 2, 5. Therefore direction ratios of line CD are given by x2 minus x1 that is 2 minus of minus 2, y2 minus y1 that is 2 minus 8, z2 minus z1 that is 5 minus of minus 3 which is equal to 4 minus 6, 8. Now here we have the value of a1, b1 and c1 given by a1 is equal to minus 2, b1 is equal to x minus 4, c1 is equal to minus 4 and value of a2, b2, c2 given by a2 is equal to 4, b2 is equal to minus 6 and c2 is equal to 8. Also we have line AB is parallel to line CD and from the key idea we know that if two lines are parallel then a1 upon a2 is equal to c1 upon c2 where a1, b1, c1 and a2, b2, c2 are the direction ratios of the two lines. Since AB is parallel to CD we have a1 upon a2 that is minus 2 upon 4 is equal to b1 upon c2 that is x minus 4 upon minus 6 is equal to c1 upon c2 that is minus 4 upon 8. Now to solve for the value of x we can either take first and second expression or second and third expression. Therefore taking second and third expression we get x minus 4 upon minus 6 is equal to minus 4 upon 8 which implies that x minus 4 upon minus 6 is equal to minus 1 upon 2 which implies that x minus 4 is equal to minus of minus 6 upon 2 which further implies that x minus 4 is equal to 3 which gives the value of x equal to 7. Therefore for x is equal to 7 the lines AB and CD will be parallel which is our final answer. This completes our session. Hope you enjoyed this session.