Three Dimensional Geometry

If the distance of the point P(43, , ), < 0, from the line r = 4 i - k + (2 i + 3 k), R along a line with direction ratios 3, -1, 0 is 13 10, then 2 + 2 is equal to

Let a line L passing through the point P(1, 1, 1) be perpendicular to the lines x-44 = y-11 = z-11 and x-171 = y-711 = z0. Let the line L intersect the yz-plane at the point Q. Another line parallel to L and passing through the point S(1, 0, -1) intersects the yz-plane at the point R. Then the square of the area of the parallelogram PQRS is equal to .

Let the area of the triangle formed by the lines x + 2 = y - 1 = z, x - 35 = y-1 = z - 11 and x-3 = y - 33 = z - 21 be A. Then A2 is equal to .

A line passes through A(4,-6,-2) and B(16,-2,4). The point P(a, b, c), where a, b, c are non-negative integers, on the line AB lies at a distance of 21 units, from the point A. The distance between the points P(a, b, c) and Q(4,-12,3) is equal to .

Let a line passing through the point (-1,2,3) intersect the lines L1: x-13= y-22= z+1-2 at M( , , ) and L2: x+2-3= y-2-2= z-14 at N(a, b, c). Then, the value of ( + + )2(a+b+c)2 equals .