Three Dimensional Geometry questions
879 published questions with worked solutions.
- A line drawn from the point A(1, 3, 2) parallel to the line x 2 = y 4 = z 1 , intersects the plane 3x+ y + 2z = 5 in point B, the...
- If A(1, 4, 2) and C(5, -7, 1) are two vertices of triangle ABC and G ( 4 3 ,0, -2 3 ) is centroid of the triangle ABC, then the...
- The distance of the point (-1, -5, -10) from the point of intersections of the line x-2 3 = y+1 4 = z-2 12 and the plane x - y +...
- The mirror image of P (2, 4, -1) in the plane x - y + 2z - 2 = 0 is (a, b, c), then the value of a + b + c is
- If the lines x-k 2 = y+1 3 = z-1 4 and x-3 1 = y- 9 2 2 = z 1 intersect, then the value of k is
- The length of the perpendicular drawn from the point (1, 2, 3) to the line x-6 3 = y-7 2 = z-7 -2 is
- If ABC is right angled at A, where A (4,2,x),B (3,1,8) and C (2,-1,2), then the value of x is
- The angle between the lines, whose direction cosines ,m,n satisfy the equation +m+n=0 and 2 ^2+2m^2-n^2=0, is
- Equation of the plane passing through (1,-1,2) and perpendicular to the planes x+2y-2z=4 and 3x+2y=6 is
- The distance of the point (1, 0,-3) from the plane x-y-z=9 measured parallel to the line x-2 2 = y+2 3 = z-6 -6 is
- The equation of the plane passing through the point (1,2,1) and perpendicular to the planes x + 2y + 2z- 7 = 0 and 3x+ 3y+ 2z- 5...
- If the lines x = -1 + s, y = 3 - s, z = 1 + s and x = t 2 , y = 1 + t, z = 2 - t with parameters s and t, are coplanar, then =
- If the lines r=( i+m j+3 k)+ (2 i+3 j+4 k) and r=(4 i+ j)+ (5 i+m j+ k) intersect each other, then m =
- If a unit vector makes angles 4 with i, 3 with j and (0, ) with k, then a value of is equal to…
- The equation of the plane containing the lines x-1 2 = y+1 = z2 and x+1 5 = y+1 2 = z is
- The direction cosines of a line which is perpendicular to the lines x-7 2 = y+17 -3 = z-6 1 and x+5 1 = y+3 2 = z-6 -2 are …
- For the line x+1 1 = y-2 2 = z+3 3 , identify the incorrect statement among the following
- If the lines x-5 5m+2 = 2-y 5 = 1-z -1 and x= 2y+1 4m = 1-z -3 are perpendicular to each other, then the value of m is…
- The perpendicular distance from the origin to the plane containing the two lines x+2 3 = y-2 5 = z+5 7 and x-1 1 = y-4 4 = z+4 7...
- Let P(2,1,5) 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 the...
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