Three Dimensional Geometry questions
879 published questions with worked solutions.
- Let P be a plane x+my+nz=0 containing the line, 1-x 1 = y+4 2 = z+2 3 . If plane P divides the line segment AB joining A(–3, –6,...
- If the equation of plane passing through the mirror image of a point (2, 3, 1) with respect to line x+1 2 = y-3 1 = z+2 -1 and...
- Let P be an arbitrary point having sum of the squares of the distance from the planes x + y + z = 0, – nz = 0 and x – 2y + z = 0,...
- If the equation of the plane passing through the line of intersection of the planes 2x – 7y + 4z – 3 = 0, 3x – 5y + 4z + 11 = 0...
- Let the mirror image of the point (1, 3, a) with respect to the plane r (2 i - j + k )-b=0 be (–3, 5, 2). Then the value of |a +...
- Let P be a plane containing the line x-1 3 = y+6 4 = z+5 2 and parallel to the line x-3 4 = y-2 -3 = z+5 7 . If the point (1, –1,...
- Let the plane ax + by + cz + d = 0 bisect the line joining the points (4, –3, 1) and (2, 3, –5) at the right angles. If a, b, c,...
- The equation of the planes parallel to the plane x – 2y + 2z – 3 = 0 which are at unit distance from the point (1, 2, 3) are ax +...
- The lines x = ay – 1 = z – 2 and x = 3y – 2 = bz – 2, (ab 0) are coplanar, if:
- Consider the line L given by the equation x-3 2 = y-1 1 = z-2 1 . Let Q be the mirror image of the point (2, 3, –1) with respect...
- Let P be a plane passing through the points (1, 0, 1), (1, –2, 1) and (0, 1, –2). let a vector a = i + j + k be such that a is...
- Let L be the line of intersection of planes r ( i - j +2 k )=2 and r (2 i + j - k )=2. If P( , , ) is the foot of perpendicular...
- Let the mirror image of the point P(a, 6, 9) with respect to the line x-3 7 = y-2 5 = z-1 -9 is (20, b, –a –9), then |a + b| is...
- Let a, b, c be in arithmetic progression. Let the centroid of the triangle with vertices (a, c), (2, b) and (a, b) be ( 10 3 , 7...
- The equation of the plane passing through the point (1, 2, –3) and perpendicular to the planes 3x + y – 2z = 5 and 2x – 5y – z =...
- The distance of the point (1, 1, 9) from the point of intersection of the line x-3 1 = y-4 2 = z-5 2 and the plane x + y + z = 17...
- Let the plane passing through the point (–1, 0, –2) and perpendicular to each of the planes 2x + y – z = 2 and x – y – z = 3 be...
- Let a plane P pass through the point (3, 7, –7) and contain the line, x-2 -3 = y-3 -3 = z+2 1 . If distance of the plane P from...
- For real number and 0, if the point of intersection of the straight lines x- 1 = y-1 2 = z-1 3 and x-4 = y-6 3 = z-7 3 , lines on...
- The distance of the point P(3, 4, 4) from the point of intersection of the line joining the points Q(3, –4, –5) and R(2, –3, 1)...
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