Equation of plane which passes through the point of intersection of l ines and and at greatest distance from the point (0, 0, 0) is
The base of the pyramid AOBC is an equilateral triangle OBA with each side equal to 4√2, 'O'is the origin of reference, AC is perpendicular to the plane of Δ OBC and = 2. Then the cosine of the angle between the skew straight lines one passing through A and the mid point of OB and the other passing through O and the mid point of BC is
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In the adjacent figure ‘P’ is any arbitrary interior point of the triangle ABC such that the lines AA_{1},BB_{1},CC_{1} are concurrent at P. Value of is always equal to
A tetrahedron has vertices at O(0, 0, 0), A(1, 2, 1), B(2, 1, 3) and C(–1, 1, 2). Then the angle between the face OAB and ABC will be
The two lines x = ay + b, z = cy + d and = a' y + b', z = c' y + d' will be perpendicular, iff
ABC is a triangle where A = (2, 3, 5), B = (–1, 2, 2) and C(λ, 5, μ). If the median through A is equally inclined to the axes then
A mirror and a source of light are situated at the origin O and at a point on OX, respectively. A ray of light from the source strikes the mirror and is reflected. If the D.r.’s of the normal to the plane are 1, –1, 1, then D.C.’s of the reflected ray are
The equation of motion of a point in space is x = 2t, y = –4t, z = 4t where t measured in hours and the coordinates of moving point in kilometers. The distance of the point from the starting point O(0, 0, 0) in 10 hours is
Minimum value of x^{2} + y^{2} + z^{2} when ax+by+cz = p is
The direction cosines of a line equally inclined to three mutually perpendicular lines having ℓ_{1}, m_{1}, n_{1}, ; ℓ_{2}, m_{2}, n_{2} ; ℓ_{3}, m_{3}, n_{3} are
The coordinates of the point where the line joining the points (2, –3, 1), (3, –4, –5) cuts the plane 2x + y + z = 7 are
If the line joining the origin and the point (–2, 1, 2) makes angle θ_{1 ,}θ_{2 }and θ_{3} with the positive direction of the coordinate axes, then the value of cos 2θ_{1} + cos 2θ_{2} + cos 2θ_{3} is
The square of the perpendicular distance of point P(p, q, r) from a line through A(a, b, c) an whose direction cosine are (ℓ) , m, n is
Equation of the plane passing through A(x_{1}, y_{1}, z_{1}) d containing the line
The equation of the line x + y + z – 1 = 0, 4x + y – 2z + 2 = 0 written in the symmetrical form is
The acute angle that the vector makes with the plane contained by the two vectors and is given by
The ratio in which the sphere x^{2} + y^{2} + z^{2} = 504 divides the line joining the points (12, –4, 8) and (27, –9, 18) is
The equation of the planes through the origin which are parallel to the line and distance 5/3 from it are
If the edges of a rectangular parallelopiped are 3, 2, 1 then the angle between a pair of diagonals is given by
Consider the lines x/2 = y/3 = z/5 and x/1 = y/2 = z/3 equation of the line which
The direction cosines of the lines bisecting the anglebetween the lines whose direction cosines are ℓ_{1}, m_{1}, n_{1} and ℓ_{2}, m_{2}, n_{2} and the angle between these lines is 0, are
The equation og line AB is . Through a point P(1, 2, 5), line PN is drawn perpendicular to AB and line PQ is drawn parallel to the plane 3x + 4y + 5z = 0 to meet AB is Q. Then
The planes 2x – 3y – 7z = 0, 3x – 14y – 13z = 0 and 8x – 31y – 33z = 0
If the length of perpendicular drawn from origin on a plane is 7 units and its direction ratios are –3, 2, 6, then that plane is
Let a perpendicular PQ be drawn from P(5, 7, 3) to the line when Q is the foot.
Then
204 videos288 docs139 tests

Distance of a point from a Plane and Angle Between a Line and a Plane  Three Dimensional Geometry Video  06:37 min 
Important Formulas  3D Geometry Doc  3 pages 
Test: Three Dimensional Geometry Assertion & Reason Type Questions Test  6 ques 
Test: Three Dimensional Geometry Case Based Type Questions 1 Test  20 ques 
Test: Three Dimensional Geometry Case Based Type Questions 2 Test  15 ques 
204 videos288 docs139 tests

Distance of a point from a Plane and Angle Between a Line and a Plane  Three Dimensional Geometry Video  06:37 min 
Important Formulas  3D Geometry Doc  3 pages 
Test: Three Dimensional Geometry Assertion & Reason Type Questions Test  6 ques 
Test: Three Dimensional Geometry Case Based Type Questions 1 Test  20 ques 
Test: Three Dimensional Geometry Case Based Type Questions 2 Test  15 ques 