List of top Mathematics Questions on Angle between a Line and a Plane

If A A and B B are the points of intersection of the circle x2+y2−8x=0 x^2 + y^2 - 8x = 0 and the hyperbola x29−y24=1 \frac{x^2}{9} - \frac{y^2}{4} = 1 , and a point P P moves on the line 2x−3y+4=0 2x - 3y + 4 = 0 , then the centroid of △PAB \triangle PAB lies on the line:
Let A and B be the two points of intersection of the line y+5=0 y + 5 = 0 and the mirror image of the parabola y2=4x y^2 = 4x with respect to the line x+y+4=0 x + y + 4 = 0 . If d d denotes the distance between A and B, and a a denotes the area of ΔSAB \Delta SAB , where S S is the focus of the parabola y2=4x y^2 = 4x , then the value of (a+d) (a + d) is:
If the equation of the plane passing through the line of intersection of the planes 2x – y + z = 3, 4x– 3y +5z + 9 = 0 and parallel to the line  x+1−2=y+34=z−25\frac{x+1}{−2} =\frac{ y+3}{4}= \frac{z−2}{5} is ax by+cz+6=0. then a + b + c is equal to 
Let the foot of perpendicular from the point A(4, 3, 1) on the plane P : x - y + 2z + 3 = 0 be N. If B(5,α,β) ∈ Z   is a point on plane P such that the area of the triangle ABN in 3√2 . then α2 + β2 + αβ is equal to ____ .
Let the line L pass through the point (0, 1, 2), intersect the line  x−12=y−23=z−34\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4} and be parallel to the plane 2x + y – 3z = 4. Then the distance of the point P(l, –9, 2) from the line L is 
A plane P contains the line of intersection of the plane  r→.(iˆ+jˆ+kˆ)=6\overrightarrow{r} .( \^i+\^j+\^k )=6 and r→.(2iˆ+3jˆ+4kˆ)=−5\overrightarrow{r }.( 2\^i+3\^j+4\^k) = − 5.  If P passes through the point (0, 2, –2), then the square of distance of the point (12, 12, 18) from the plane P is 
Let the plane P : 4x – y + z = 10 be rotated by an angle π2\frac{π}{2} about its line of intersection with the plane x + y – z = 4. If α is the distance of the point (2, 3, -4) from the new position of the plane P, then 35α is
Let A be the point (0,4) in the xy-plane and B be the point (2t,0). Let L be AB's midpoint and let AB's perpendicular bisector meet the y-axis M. Let N be the midpoint of LM. The locus of N is
The angle between a normal to the plane 2x-y+2z-1=0 and the X-axis is 
Let the plane x + 3y – 2z + 6 = 0 meet the co-ordinate axes at the points A,B,C. If the orthocentre of the triangle ABC is (α,β,67),(α,β,\frac{6}{7}), then 98(α + β)2 is equal to___.
If the straight line y=mx+c y = mx + c touches the parabola y2−4ax+4a3=0 y^2 - 4ax + 4a^3 = 0 , then c c is:
Let a1,a2,a3,… a_1, a_2, a_3, \dots be a harmonic progression with a1=5 a_1 = 5 and a20=25 a_{20} = 25 . The least positive integer n n for which an<0 a_n<0 is:
If g(x)=x2+x−2 g(x) = x^2 + x - 2 and 12g∘f(x)=2x2−5x+2, \frac{1}{2} g \circ f(x) = 2x^2 - 5x + 2, then f(x) f(x) is equal to:
If in a △ABC \triangle ABC , 2b2=a2+c2 2b^2 = a^2 + c^2 , then
sin⁡3Bsin⁡Bisequalto: \frac{\sin 3B}{\sin B} { is equal to:}
The area enclosed by the curves y=sin⁡x+cos⁡x y = \sin x + \cos x { and } y=∣cos⁡x−sin⁡x∣ y = | \cos x - \sin x | { over the interval} [0,π2] \left[ 0, \frac{\pi}{2} \right] { is:}
Let P be the plane containing the straight line x−39\frac{ x−3}{9}=y+4−1\frac{y+4}{-1}=z−7−5\frac{z-7}{-5}and perpendicular to the plane containing the straight lines x2=y3=z5\frac{x}{2}=\frac{y}{3}=\frac{z}{5} and x3=y7=z8\frac{x}{3}=\frac{y}{7}=\frac{z}{8}.If d is the distance P from the point (2, –5, 11), then d2 is equal to :
LetA(1,1),B(−4,3) A(1, 1), B(-4, 3) and C(−2,−5)C(-2, -5) be vertices of a triangle ABC, P be a point on side BC, and Δ1Δ1 and Δ2Δ2 be the areas of triangles APB and ABC, respectively. If Δ1 :Δ2 =4:7Δ1 : Δ2 = 4 : 7, then the area enclosed by the lines AP, AC and the x-axis is
A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semi-vertical angle is tan-1(3/4). Water is poured in it at a constant rate of 6 cubic meter per hour. The rate (in square meter per hour), at which the wet curved surface area of the tank is increasing, when the depth of water in the tank is 4 meters, is

Let a vertical tower AB of height 2h stands on a horizontal ground. Let from a point P on the ground a man can see up to height h of the tower with an angle of elevation 2α.
When from P, he moves a distance d in the direction of AP→\overrightarrow{AP}.
he can see the top B of the tower with an angle of elevation α. if d=7d = \sqrt7 h, then tan α is equal to

If the plane P passes through the intersection of two mutually perpendicular planes 2x + ky – 5z = 1 and 3kx – ky + z = 5, k < 3 and intercepts a unit length on positive x-axis, then the intercept made by the plane P on the y-axis is

If one of the lines ax2+2hxy+by2=0 bisects the angle between positive directions of the axes then a,h,b satisfy the relation
The equation of the plane which bisects the line joining (3, 0, 5) and (1,2,-1) at right angles is
If the angle θ between the line x+11=y−12=z−22 and the plane 2x−y+λz+4=0 is such that sin⁡θ=13, then value of λ is
The angle between the line 3x−13=y+3−1 \frac{3x-1}{3}=\frac{y+3}{-1} =5−2z4 =\frac{5-2z}{4} and the plane 3x−3y−6z=10 3x-3y-6z=10 is equal to
The sine of the angle between the straight line x−23=y−34=4−z−5\frac{x-2}{3}=\frac{y-3}{4}=\frac{4-z}{-5} are the plane 2x-2y+z=5 is