# Three Dimensional Geometry

### If the image of the point P(1, –2, 3) in the plane, 2x + 3y – 4z + 22 = 0

If the image of the point P(1, –2, 3) in the plane, 2x + 3y – 4z + 22 = 0 measured parallel to the line, x/1 = y/4 = z/5 is Q, then PQ is equal to:

1. 3√5
2. 2√42
3. √42
4. 6√5

### The angle between the lines whose direction cosines satisfy

The angle between the lines whose direction cosines satisfy the equations l + m + n = 0 and l2 + m2 + n2 = 0 is

1. π/2
2. π/3
3. π/4
4. π/6

### If the lines (x-1)/2 = (y+1)/2 = (z-1)/4 and (x-3)/1 = (y-k)/2 = z/1

If the lines (x - 1)/2 = (y + 1)/2 = (z - 1)/4 and (x - 3)/1 = (y - k)/2 = z/1 intersect, then k is equal to

1. 9/2
2. 2/9
3. -1
4. 0

### If the angle between the line x = (y - 1)/2 = (z - 3)/λ and the plane

If the angle between the line x = (y - 1)/2 = (z - 3)/λ and the plane x + 2y + 3z = 4 is cos-1(5/14) then λ is equal to

1. 3/2
2. 2/5
3. 2/3
4. 5/3

### A line AB in three-dimensional space makes angles 45° and 120°

A line AB in three-dimensional space makes angles 45° and 120° with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle θ with the positive z-axis, then θ equals

1. 30°
2. 45°
3. 60°
4. 75°

### Let the line (x - 2)/3 = (y - 1)/-5 = (z - 2)/2 lie in the plane

Let the line (x - 2)/3 =  (y - 1)/-5 =  (z - 2)/2 lie in the plane x + 3y - αz + β = 0. Then (α, β) equals

1. (-5, 5)
2. (5, -15)
3. (-6, 7)
4. (6, -17)

### The distance of the point (1,0,2) from the point of intersection

The distance of the point (1,0,2) from the point of intersection of the line (x - 2)/3 = (y + 1)/4 = (z - 2)/12 and the plane x - y + z = 16 is

1. 13
2. 8
3. 3√21
4. 2√14

### A plane which passes through the point (3, 2, 0) and the line (x-4)/1 = (y-7)/5 = (z-4)/4 is

A plane which passes through the point (3, 2, 0) and the line (x-4)/1 = (y-7)/5 = (z-4)/4 is

1. 2x - y + z = 5
2. x + 2y - z = 1
3. x - y + z = 1
4. x + y + z = 5

### If the line lies in the plane, lx + my – z = 9, then l^2 + m^2 is equal to

If the line, (x-3)/2 = (y+2)/-1 = (z+4)/3, lies in the plane, lx + my – z = 9, then l2 + m2 is equal to:

1. 18
2. 5
3. 2
4. 26