Three Dimensional Geometry questions
879 published questions with worked solutions.
- Let the image of the point P(1, 2, 3) in the line L : (x − 6)/3 = (y − 1)/2 = (z − 2)/3 be Q. Let R( , , ) be a point that...
- If two distinct points Q, R lie on the line of intersection of the planes −x + 2y − z = 0 and 3x − 5y + 2z = 0 and PQ = PR = 18...
- The acute angle between the planes P_ 1 and P_ 2 , when P_ 1 and P_ 2 are the planes passing through the intersection of the...
- Let Q be the foot of perpendicular drawn from the point P(1, 2, 3) to the plane x + 2y + z = 14. If R is a point on the plane...
- If the foot of the perpendicular from the point A(−1, 4, 3) on the plane P : 2x + my + nz = 4, is (−2, 7/2, 3/2), then the...
- Let a line with direction ratios a, −4a, −7 be perpendicular to the lines with direction ratios 3, −1, 2b and b, a, −2. If the...
- Let (x − 2)/3 = (y + 1)/(−2) = (z + 3)/(−1) lie on the plane px − qy + z = 5, for some p, q R. The shortest distance of the plane...
- The distance of the origin from the centroid of the triangle whose two sides have the equations x − 2y + 1 = 0 and 2x − y − 1 = 0...
- Let Q be the mirror image of the point P(1, 2, 1) with respect to the plane x + 2y + 2z = 16. Let T be a plane passing through...
- If the mirror image of the point (2, 4, 7) in the plane 3x − y + 4z = 2 is (a, b, c), then 2a + b + 2c is equal to :
- Let P_ 1 : r (2 i + j - 3 k ) = 4 be a plane. Let P_ 2 be another plane which passes through the points (2, −3, 2), (2, −2, −3)...
- The centroid of the triangle with vertices A(2, -3, 3), B(5, -3, -4) and C(2, -3, -2) is the point
- The equation of the plane passing through the intersection of the planes 2x+y+2z=9, 4x-5y-4z=1 and the point (3, 2, 1) is
- The distance between the parallel planes 4x-2y+4z+9=0 and 8x-4y+8z+21=0 is
- What are the direction cosines of z-axis?
- If the equation of the plane passing through the line of intersection of the planes 2x – y + z = 3, 4x – 3y + 5z + 9 = 0 and...
- Let the image of the point P(1, 2, 3) in the plane 2x – y + z = 9 be Q. If the coordinates of the point R are (6, 10, 7), then...
- For a, b Z and |a-b| 10, let the angle between the plane P : ax + y – z = b and the line : x – 1 = a – y = z + 1 be ^ -1 ( 1 3 )....
- The area of the quadrilateral ABCD with vertices A(2, 1, 1), B(1, 2, 5), C(–2, –3, 5) and D(1, –6, –7) is equal to
- Let P be the plane passing through the line x-1 1 = y-2 -3 = z+5 7 and the point (2, 4, –3). If the image of the point (–1, 3, 4)...
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