Three Dimensional Geometry questions
879 published questions with worked solutions.
- The equation of the plane containing the line x - 2 3 = y + 1 2 = z - 4 -2 and the point (0, 5, 0) is
- If the angle between the line x= y-1 2 = z-3 and the plane x+2y+3z=4 is ^ -1 5 14 , then the value of is
- The angle between the lines x - 3y - 4 = 0, 4y - z + 5 = 0 and x + 3y - 11 = 0, 2y - z + 6 = 0 is
- The projection of the line segment joining P(2, -1, 0) and Q (3, 2, -1) on the line whose direction ratios are 1, 2, 2 is
- The line L is passing through (1, 2, 3). The distance of any point on the line L from the line r=(3 -1) i+(-2 +3) j+(4+ ) k is...
- If the lines x-1 2 = y+1 k = z 2 and x+1 5 = y+1 2 = z k are coplanar, then the equation of the plane containing these lines are
- Let the line x-2 3 = y-1 -5 = z+2 2 lie in the plane x+3y- z+ =0, then the value of ( - ) is equal to
- If the planes r (2 i - j + k )=3 and r (4 i - j + k )=5 are parallel, then + =
- The perimeter of a square whose two sides have equations x-1 2 = y+2 3 = z-3 4 and x 2 = y-1 3 = z+1 4 is
- If the sum of the squares of the distances of a point P(x,y,z) from the three co-ordinate axes is 324, then the distance of point...
- If is the angle between the lines whose direction cosines are given by 6mn-2nl+5lm=0 and 3l+m+5n=0, then =
- The line passing through the points (a,1,6) and (3,4,b) crosses the yz-plane at (0, 17 2 , -13 2 ), then the value of (3a+4b) is
- If the foot of the perpendicular drawn from the origin to a plane is P(2,-1,4) then the equation of the plane is
- Let the plane passing through point (2,1,-1) containing line joining the points (1,3,2) and (1,2,1) makes intercepts p, q, r on...
- The angle between the line x= y-1 2 = z-3 and the plane x+2y+3z=6 is ^ -1 5 14 , then the value of is
- The equation of the line passing through the point of intersection of x-1 2= y-2 3= z-3 4 and x-4 5= y-1 2=z and also through the...
- If the lines x-1 2= y+1 3= z-1 4 and x-3 1= y-k 2= z1 intersect, then the value of k is
- The equation of the plane containing the line x1= y2= z3 and perpendicular to the plane containing the lines x2= y3= z1 and x3=...
- The equation of the plane containing the line x+1 2= y+2 1= z-2 3 and the point (1,-1, 3) is
- If the plane x 2 - y 3 - z 5 = 1 cuts the co-ordinate axes in point A, B, C respectively, then the area of the triangle ABC is
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