Three Dimensional Geometry

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 )

Let L1: x-13= y-1-1= z+10 and L2: x-22= y0= z+4 , , be two lines, which intersect at the point B. If P is the foot of perpendicular from the point A(1,1,-1) on L2, then the value of 26 (PB)2 is .

Let a line pass through two distinct points P(-2,-1,3) and Q, and be parallel to the vector 3 i+2 j+2 k. If the distance of the point Q from the point R(1,3,3) is 5, then the square of the area of PQR is equal to :

1. 148
2. 144
3. 136
4. 140

The perpendicular distance, of the line x-12= y+2-1= z+32 from the point P(2,-10,1), is :

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

The shortest distance between the lines x - 34 = y + 7-11 = z - 15 and x - 53 = y - 9-6 = z + 21 is:

1. 185 563
2. 187 563
3. 178 563
4. 179 563

Let the line L intersect the lines x - 2 = -y = z - 1, 2(x + 1) = 2(y - 1) = z + 1 and be parallel to the line x - 23 = y - 11 = z - 22. Then which of the following points lies on L ?

1. (- 13, 1, -1 )
2. (- 13, -1, 1 )
3. (- 13, -1, -1 )
4. (- 13, 1, 1 )