JEE Advanced Level Test: Three Dimensional 3D Geometry- 3 - JEE MCQ

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 co-ordinates 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 x² + y² + z² when ax+by+cz = p is

The direction cosines of a line equally inclined to three mutually perpendicular lines having ℓ₁, m₁, n₁, ; ℓ₂, m₂, n₂ ; ℓ₃, m₃, n₃ are

The co-ordinates 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 ,}θ₂ and θ₃ with the positive direction of the coordinate axes, then the value of cos 2θ₁ + cos 2θ₂ + cos 2θ₃ 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(x₁, y₁, z₁) 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 x² + y² + z² = 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 ℓ₁, m₁, n₁ and ℓ₂, m₂, n₂ 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