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

The shortest distance between the lines x - 32 = y + 15-7 = z - 95 and x + 12 = y - 11 = z - 9-3 is

1. 8 3
2. 6 3
3. 5 3
4. 4 3

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

If the shortest distance between the lines x - 3 = y - 2-1 = z - 11 and x + 2-3 = y + 52 = z - 44 is 44 30, then the largest possible value of | | is equal to .

If the line 2 - x3 = 3y - 24 + 1 = 4 - z makes a right angle with the line x + 33 = 1 - 2y6 = 5 - z7, then 4 + 9 is equal to :

1. 4
2. 13
3. 5
4. 6

Let d be the distance of the point of intersection of the lines x + 63 = y2 = z + 11 and x - 74 = y - 93 = z - 42 from the point (7, 8, 9). Then d2 + 6 is equal to :

1. 75
2. 78
3. 72
4. 69

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 the point (-1, , ) lie on the line of the shortest distance between the lines x + 2-3 = y - 24 = z - 52 and x + 2-1 = y + 62 = z - 10. Then ( - )2 is equal to .

Let the point, on the line passing through the points P(1,-2,3) and Q(5,-4,7), farther from the origin and at a distance of 9 units from the point P, be ( , , ). Then 2+ 2+ 2 is equal to :

1. 150
2. 155
3. 160
4. 165