Three Dimensional Geometry questions
879 published questions with worked solutions.
- ABCDEFGH is a cuboid with base ABCD. Let A(0, 0, 0), B(12, 0, 0), C(12, 6, 0) and G(12, 6, 4) be the vertices. If is the angle...
- Let , , , be real numbers such that ^2 + ^2 + ^2 0 and + = 1. Suppose the point (3, 2, -1) is the mirror image of the point (1,...
- Let P_1 and P_2 be two planes given by P_1: 10x + 15y + 12z - 60 = 0, P_2: -2x + 5y + 4z - 20 = 0. Which of the following...
- Let S be the reflection of a point Q with respect to the plane given by r = -(t + p) i + t j + (1 + p) k where t, p are real...
- Let _1 and _2 be the lines r _1 = ( i + j + k ) and r _2 = ( j - k ) + ( i + k ), respectively. Let X be the set of all the...
- Let R ^3 denote the three-dimensional space. Take two points P = (1, 2, 3) and Q = (4, 2, 7). Let dist(X, Y) denote the distance...
- A straight line drawn from the point P(1, 3, 2), parallel to the line x-2 1 = y-4 2 = z-6 1 , intersects the plane L_1: x - y +...
- If the length of the perpendicular drawn from the point P(a, 4, 2), a > 0 on the line (x + 1)/2 = (y − 3)/3 = (z − 1)/(−1) is 2 6...
- If the line of intersection of the planes ax + by = 3 and ax + by + cz = 0, a > 0 makes an angle 30° with the plane y − z + 2 =...
- If the plane P passes through the intersection of two mutually perpendicular planes 2x + ky − 5z = 1 and 3kx − ky + z = 5, k < 3...
- Let the line (x − 3)/7 = (y − 2)/(−1) = (z − 3)/(−4) intersect the plane containing the lines (x − 4)/1 = (y + 1)/(−2) = z/1 and...
- Let the foot of the perpendicular from the point (1, 2, 4) on the line (x + 2)/4 = (y − 1)/2 = (z + 1)/3 be P. Then the distance...
- In an isosceles triangle ABC, the vertex A is (6, 1) and the equation of the base BC is 2x + y = 4. Let the point B lie on the...
- If two straight lines whose direction cosines are given by the relations l + m − n = 0, 3l^ 2 + m^ 2 + cnl = 0, are parallel,...
- Let the mirror image of the point (a, b, c) with respect to the plane 3x − 4y + 12z + 19 = 0 be (a − 6, , ). If a + b + c = 5,...
- Let the lines (x - 1)/ = (y − 2)/1 = (z − 3)/2 and (x + 26)/(−2) = (y + 18)/3 = (z + 28)/ be coplanar and P be the plane...
- A plane P is parallel to two lines whose direction rations are −2, 1, −3 and −1, 2, −2 and it contains the point (2, 2, −2). Let...
- The foot of the perpendicular from a point on the circle x^ 2 + y^ 2 = 1, z = 0 to the plane 2x + 3y + z = 6 lies on which one of...
- Let P(−2, −1, 1) and Q(56/17, 43/17, 111/17) be the vertices of the rhombus PRQS. If the direction ratios of the diagonal RS are...
- Let the plane ax + by + cz = d pass through (2, 3, −5) and is perpendicular to the planes 2x + y − 5z = 10 and 3x + 5y − 7z = 12....
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