Three Dimensional Geometry questions
879 published questions with worked solutions.
- If the points A(1, 2, -1), B(2, 6, 2) and C( , -2, -4) are collinear then is
- If A = (1, 1, 1), B = (2, -1, 3), C = (0, 4, -2), D = (1, 2, ) and AB, AC and AD are coplanar then is
- The angle between the lines joining the points (1, 1, 0), (3, 3 + 1, 3), and (0, -1, 0), (-1, 3 - 1, ) is ^ -1 ( 18 ). If is an...
- l_r, m_r, n_r; r = 1, 2, 3; are the direction cosines of three mutually perpendicular lines. The direction cosines of the line...
- Let A = (1, 2, 2), B = (2, 3, 6) and C = (3, 4, 12). The direction cosines of a line equally inclined with OA, OB and OC where O...
- The angle between the lines whose direction cosines satisfy the equations l + m + n = 0 and l^2 = m^2 + n^2 is
- The value of for which the triangle ABC whose vertices are A(6, 10, 10), B(1, 0, -5) and C(6, -10, ) is right-angled at B, is
- Let A = (1, 2, 3), B = (-1, -2, -1), C = (2, 3, 2) and D = (4, 7, 6). Then ABCD is a
- If A = (5, -1, 1), B = (7, -4, 7), C = (1, -6, 10), D = (-1, -3, 4) then ABCD is a
- If A = (0, 0, 2), B = ( 2, 2, 2), C = ( 2, 2, 0) and D = ( 8 2 - 20 17 , 12 2 + 4 17 , 20 - 8 2 17 ) then ABCD is a
- If the vertices of a triangle are (-1, 6, -4), (2, 1, 1) and (5, -1, 0) then the centroid of the triangle is
- If two vertices of a triangle ABC are A(-1, 2, 4) and B(2, -3, 0), and the centroid is (2, 0, 2) then the vertex C has the...
- Four vertices of a tetrahedron are (0, 0, 0), (4, 0, 0), (0, -8, 0) and (0, 0, 12). Its centroid has the coordinates
- Three vertices of a tetrahedron are (0, 0, 0), (6, -5, -1) and (-4, 1, 3). If the centroid of the tetrahedron be (1, -2, 5) then...
- The points A(1, 2, -1), B(2, 5, -2), C(4, 4, -3) and D(3, 1, -2) are
- ABC is a triangle where A = (2, 3, 5), B = (-1, 3, 2) and C = ( , 5, ). If the median through A is equally inclined with the axes...
- Let P_r(x_r, y_r, z_r); r = 1, 2, 3; be three points where x_1, x_2, x_3; y_1, y_2, y_3 and z_1, z_2, z_3 are each in GP with the...
- A point Q at a distance 3 from the point P(1, 1, 1) lying on the line joining the points A(0, -1, 3) and P, has the coodinates
- If the direction ratios of a line are 1 + , 1 - , 2, and it makes an angle of 60^ with the y-axis then is
- The direction cosines of a line whose equations are x-1 2 = y+3 4 = z-2 -3 are
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