If d is the distance of point (2, 5, 10) from the plane containing the lines r = (4 j - k ) + ( i + 2 j - 2 k ) and r = (2 i + j ) + ( i + 2 j - 2 k ) , then d^2 =

Step-by-step solution

The given lines are: r = (4 j - k ) + ( i + 2 j - 2 k ) r = (2 i + j ) + ( i + 2 j - 2 k ) The lines are parallel with direction vector b = i + 2 j - 2 k . Let A(0, 4, -1) be a point on the first line and B(2, 1, 0) be a point on the second line. The vector joining A and B is AB = 2 i - 3 j + k . The normal vector n to the plane containing these two lines is perpendicular to both b and AB : n = b AB = vmatrix i & j & k 1 & 2 & -2 2 & -3 & 1 vmatrix n = i (2 - 6) - j (1 - (-4)) + k (-3 - 4) = -4 i - 5 j - 7 k Taking