Three Dimensional Geometry

A line with direction ratios 1, -1, 2 intersects the lines x2= y3= z+13 and x+1-1= y-21= z4 at the points P and Q, respectively. If the length of the line segment PQ is , then 225 2 is equal to:

1. 1024
2. 1014
3. 1104
4. 1204

The square of the distance of the point (-2, -8, 6) from the line x-11= y-12= z-1 along the line x+51= y+5-1= z2 is equal to:

1. 3
2. 6
3. 8
4. 12

The shortest distance between the lines r= ( 13 i+2 j+ 83 k )+ (2 i-5 j+6 k ) and r= (- 23 i- 13 k )+ ( j- k ), , R, is :

1. 5
2. 3
3. 2 3
4. 15

If (2 +1, 2-3 , -12 ) is the image of ( , 2 , 1) in the line x-23= y-12= z1, then the possible value(s) of is (are)

1. Only 3
2. Only 3 and -1
3. Only 3, 14 and -1
4. Only 3 and 14

If the point of intersection of the lines x+13= y+a5= z+b+17 and x-21= y-b4= z-2a7 lies on xy-plane, then the value of a+b is :

1. 2
2. 5
3. 7
4. 9

Let a line L passing through the point (1, 1, 1) be perpendicular to both the vectors 2 i+2 j+ k and i+2 j+2 k. If P(a, b, c) is the foot of perpendicular from the origin on the line L, then the value of 34(a+b+c) is :

1. 50
2. 80
3. 100
4. 120

Let the point A be the foot of perpendicular drawn from the point P(a, b, 0) on the line x-12= y-21= z- 3. If the midpoint of the line segment PA is (0, 34, - 14 ), then the value of a2+b2+ 2 is equal to :

1. 1
2. 2
3. 6
4. 9

If the distances of the point (1, 2, a) from the line x - 11 = y2 = z - 11 along the lines L1 : x - 13 = y - 24 = z - ab and L2 : x - 11 = y - 24 = z - ac are equal, then a + b + c is equal to

1. 4
2. 6
3. 7
4. 5

Let Q(a, b, c) be the image of the point P(3, 2, 1) in the line x - 11 = y2 = z - 11. Then the distance of Q from the line x - 93 = y - 92 = z - 5-2 is

1. 8
2. 7
3. 6
4. 5

If the distance of the point P(43, , ), < 0, from the line r = 4 i - k + (2 i + 3 k), R along a line with direction ratios 3, -1, 0 is 13 10, then 2 + 2 is equal to