Three Dimensional Geometry questions
879 published questions with worked solutions.
- If the direction cosines <l, m, n> of a line are connected by relation l+2m+n=0, 2l-2m+3n=0, then what is the value of...
- If a vector of magnitude 2 units makes an angle 3 with 2 i , 4 with 3 j and an acute angle with 4 k , then what are the...
- If p and q are real numbers between 0 and 1 such that the points (p, 1), (1, q) and (0, 0) form an equilateral triangle, then...
- If a line in 3 dimensions makes angles , and with the positive directions of the coordinate axes, then what is ( + ) ( - ) equal...
- A(1, 2, -1), B(2, 5, -2) and C(4, 4, -3) are three vertices of a rectangle. What is the area of the rectangle?
- ABC is a triangle right-angled at B. If A(k, 1, -1), B(2k, 0, 2) and C(2+2k, k, 1) are the vertices of the triangle, then what is...
- If a line x+1 p = y-1 q = z-2 r where p=2q=3r, makes an angle with the positive direction of y-axis, then what is 2 equal to?
- What is the equation of the plane passing through the point (1, 1, 1) and perpendicular to the line whose direction ratios are 3,...
- If the vertices B and D of a square ABCD are (2, 3) and (4, 1) respectively, then what is the area of the square?
- A line makes angles , and with the positive directions of x-axis, y-axis and z-axis respectively such that + =90^ . Which of the...
- What is the area of the triangle whose vertices are (0, 7, 10), (-1, 6, 6) and (-4, 9, 6)?
- If O is the origin and P is the point (2, -4, 6), then what is the equation of the plane through P and perpendicular to OP?
- The image of the point P(1, 3, 4) with respect to the plane Ax+By+Cz+D=0 is (-3, 5, 2). If A+B+C=2, then what is D equal to?
- How much angle does r =( ) i +( ) j + k make with the positive direction of z-axis?
- If l, m, n are the direction cosines of the line x-1=2(y+3)=1-z, then what is l^4+m^4+n^4 equal to?
- What is the projection of the line segment joining A(1, 7, -5) and B(-3, 4, -2) on y-axis?
- What is the number of possible values of k for which the line joining the points (k, 1, 3) and (1, -2, k+1) also passes through...
- The foot of the perpendicular drawn from the origin to the plane x+y+z=3 is
- The locus of a point P(x, y, z) which moves in such a way that z=7 is a
- Consider the following statements : 1. A line in space can have infinitely many direction ratios. 2. It is possible for certain...
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