Three Dimensional Geometry

Let O be the origin, and M and N be the points on the lines x-54= y-41= z-53 and x+812= y+25= z+119 respectively such that MN is the shortest distance between the given lines. Then OM ON is equal to .

The distance of the point (7,-2,11) from the line x-61= y-40= z-83 along the line x-52= y-1-3= z-56, is :

1. 12
2. 18
3. 21
4. 14

If the shortest distance between the lines x-41= y+12= z-3 and x- 2= y+14= z-2-5 is 6 5, then the sum of all possible values of is :

1. 10
2. 5
3. 7
4. 8

Let the position vectors of the vertices A, B and C of a triangle be 2 i+2 j+ k, i+2 j+2 k and 2 i+ j+2 k respectively. Let l1, l2 and l3 be the lengths of perpendiculars drawn from the orthocentre of the triangle on the sides AB, BC and CA respectively, then l12+l22+l32 equals:

1. 14
2. 15
3. 13
4. 12

Let the image of the point (1,0,7) in the line x1= y-12= z-23 be the point ( , , ). Then which one of the following points lies on the line passing through ( , , ) and making angles 2 3 and 3 4 with y-axis and z-axis respectively and an acute angle with x-axis ?

1. (1,-2,1+ 2 )
2. (3,-4,3+2 2 )
3. (3,4,3-2 2 )
4. (1,2,1- 2 )

The lines x-22= y-2= z-716 and x+34= y+23= z+21 intersect at the point P. If the distance of P from the line x+12= y-13= z-11 is l, then 14l2 is equal to .