Three Dimensional Geometry

Let P( , , ) be the image of the point Q(1, 6, 4) in the line x1 = y - 12 = z - 23. Then 2 + + is equal to

Let P be the point (10, -2, -1) and Q be the foot of the perpendicular drawn from the point R(1, 7, 6) on the line passing through the points (2, -5, 11) and (-6, 7, -5). Then the length of the line segment PQ is equal to .

Let P( , , ) be the image of the point Q(3, -3, 1) in the line x - 01 = y - 31 = z - 1-1 and R be the point (2, 5, -1). If the area of the triangle PQR is and 2 = 14K, then K is equal to :

1. 18
2. 81
3. 72
4. 36

Let ( , , ) be the image of the point (8, 5, 7) in the line x - 12 = y + 13 = z - 25. Then + + is equal to :

1. 16
2. 20
3. 18
4. 14

Let P be the point of intersection of the lines x - 21 = y - 45 = z - 21 and x - 32 = y - 23 = z - 32. Then, the shortest distance of P from the line 4x = 2y = z is

1. 3 147
2. 5 147
3. 147
4. 6 147

Consider a line L passing through the points P(1, 2, 1) and Q(2, 1, -1). If the mirror image of the point A(2, 2, 2) in the line L is ( , , ), then + + 6 is equal to .

If the mirror image of the point P(3,4,9) in the line x-13= y+12= z-21 is ( , , ), then 14( + + ) is :

1. 102
2. 138
3. 132
4. 108

The distance of the point Q(0,2,-2) from the line passing through the point P(5,-4,3) and perpendicular to the lines r=(-3 i+2 k)+ (2 i+3 j+5 k), R and r=( i-2 j+ k)+ (- i+3 j+2 k), R is :

1. 74
2. 86
3. 54
4. 20

Let Q and R be the feet of perpendiculars from the point P(a, a, a) on the lines x=y, z=1 and x=-y, z=-1 respectively. If is a right angle, then 12a2 is equal to .

Let ( , , ) be the mirror image of the point (2,3,5) in the line x-12= y-23= z-34. Then, 2 +3 +4 is equal to

1. 32
2. 31
3. 33
4. 34

Let ( , , ) be the foot of perpendicular from the point (1,2,3) on the line x+35= y-12= z+43. Then 19( + + ) is equal to :

1. 99
2. 102
3. 101
4. 100

A line with direction ratios 2,1,2 meets the lines x=y+2=z and x+2=2y=2z respectively at the points P and Q. If the length of the perpendicular from the point (1,2,12) to the line PQ is l, then l2 is .

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

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 .