Three Dimensional Geometry

Let P be the foot of the perpendicular from the point (1,2,2) on the line L: x-11= y+1-1= z-22. Let the line r= (- i+ j-2 k )+ ( i- j+ k ), , intersect the line L at Q. Then 2(PQ)2 is equal to :

1. 25
2. 27
3. 19
4. 29

If the image of the point (4, 4, 3) in the line x - 12 = y - 21 = z - 13 is ( , , ), then + + is equal to

1. 12
2. 9
3. 7
4. 8

The square of the distance of the point ( 157, 327, 7 ) from the line x+13 = y+35 = z+57 in the direction of the vector i + 4 j + 7 k is:

1. 66
2. 54
3. 41
4. 44

Let in a ABC, the length of the side AC be 6, the vertex B be (1,2,3) and the vertices A, C lie on the line x-63= y-72= z-7-2. Then the area (in sq. units) of ABC is:

1. 42
2. 17
3. 56
4. 21

Let the line passing through the point (-1,2,1) and parallel to the line x-12= y+13= z4 intersect the line x+23= y-32= z-41 at the point P. Then the distance of P from the point Q(4,-5,1) is

1. 5 6
2. 5
3. 5 5
4. 10

Let P be the image of the point Q(7,-2,5) in the line L: x-12= y+13= z4 and R(5,p,q) be a point on L. Then the square of the area of PQR is .

Let P be the foot of the perpendicular from the point Q(10,-3,-1) on the line x-37= y-2-1= z+1-2. Then the area of the right angled triangle PQR, where R is the point (3,-2,1), is

1. 30
2. 9 15
3. 3 30
4. 8 15

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 )