Three Dimensional Geometry · Question 7

The square of the distance of the point of intersection of the lines r= ( i+ j- k )+ (a i- j ), a 0 and r= (4 i- k )+ (2 i+a k ) from the origin is :

1. 5
2. 10
3. 17
4. 26

Let a triangle PQR be such that P and Q lie on the line x+38= y-42= z+12 and are at a distance of 6 units from R(1, 2, 3). If ( , , ) is the centroid of PQR, then + + is equal to :

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

If the distance of the point (a, 2, 5) from the image of the point (1, 2, 7) in the line x1= y-11= z-22 is 4, then the sum of all possible values of a is equal to :

1. 11
2. 9
3. 6
4. 4

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