Three Dimensional Geometry

If the square of the shortest distance between the lines x-21= y-12= z+3-3 and x+12= y+34= z+5-5 is mn, where m, n are coprime numbers, then m+n is equal to :

1. 14
2. 6
3. 21
4. 9

The distance of the line x-22= y-63= z-34 from the point (1,4,0) along the line x1= y-22= z+33 is :

1. 17
2. 13
3. 15
4. 14

Let L1: x-12= y-23= z-34 and L2: x-23= y-44= z-55 be two lines. Then which of the following points lies on the line of the shortest distance between L1 and L2 ?

1. ( 143,-3, 223 )
2. (2,3, 13 )
3. ( 83,-1, 13 )
4. (- 53,-7,1 )

Let L1: x-13= y-1-1= z+10 and L2: x-22= y0= z+4 , , be two lines, which intersect at the point B. If P is the foot of perpendicular from the point A(1,1,-1) on L2, then the value of 26 (PB)2 is .

Let a line pass through two distinct points P(-2,-1,3) and Q, and be parallel to the vector 3 i+2 j+2 k. If the distance of the point Q from the point R(1,3,3) is 5, then the square of the area of PQR is equal to :

1. 148
2. 144
3. 136
4. 140

The perpendicular distance, of the line x-12= y+2-1= z+32 from the point P(2,-10,1), is :

1. 6
2. 4 3
3. 3 5
4. 5 2