Three Dimensional Geometry questions
879 published questions with worked solutions.
- Let L be the line of intersection of the planes 2x + 3y + z = 1 and x + 3y + 2z = 2. If L makes an angles with the positive...
- If a line makes an angle of 4 with the positive directions of each of x-axis and y-axis, then the angle that the line makes with...
- The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz− plane at the point (0, 17 2 , -13 2 ). Then
- If the straight lines x - 1 k = y - 2 2 = z - 3 3 and x - 2 3 = y - 3 k = z - 1 2 intersect at a point, then the integer k is...
- Let the line x - 2 3 = y - 1 -5 = z + 2 2 lies in the plane x + 3y - z + = 0. Then ( , ) equals
- The projections of a vector on the three coordinate axis are 6, −3, 2 respectively. The direction cosines of the vector are
- Statement-1: The point A(3, 1, 6) is the mirror image of the point B(1, 3, 4) in the plane x − y + z = 5. Statement-2: The plane...
- A line AB in three-dimensional space makes angles 45° and 120° with the positive x-axis and the positive y-axis respectively. If...
- If the angle between the line x = y - 1 2 = z - 3 and the plane x + 2y + 3z = 4 is ^ -1 ( 5 14 ), then λ equals
- This question has Statement −1 and Statement −2. Of the four choices given after the statements, choose the one that best...
- The equation of the plane, passing through the mid point of the line segment of join of the points P (1,2,3) and Q (3,4,3) and...
- The area of the triangle, whose vertices are A (1,-1,2), B (2,1,-1) and C (3,-1,2), is
- Let P be the image of the point (3,1,7) with respect to the plane x-y+z=3. Then the equation of the plane passing through P and...
- The Cartesian equation of the plane, passing through the points (3, 1, 1), (1, 2, 3) and (-1, 4, 2) is
- The equation of the line passing through the point (-1, 3,-2) and perpendicular to each of the lines x 1 = y 2 = z 3 and x+2 -3 =...
- If the line x-3 2 = y+2 -1 = z+4 3 lies in the plane x+my-z=9, then ^2+m^2 is
- The equation of the plane passing through the point (1, 1, 1) and perpendicular to the planes 2x - y - 2z = 5 and 3x - 6y + 2z =...
- If A (-4, 5, P), B (3, 1, 4) and C (-2, 0, q) are the vertices of a triangle ABC and G (r, q, 1) is its centroid, then the value...
- Let P (2,3,6) be a point in space and Q be a point on the line r =( i - j +2 k )+ (-3 i + j +5 k ). Then the value of for which...
- If A (1,-1,0),B (0,1,-1) and C (-1,0,1), then the unit vector d such that a and d are perpendiculars and b , c , d are coplanar is
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