Three Dimensional Geometry
Let L be the line of intersection of the planes 2x+3y+z=1 and x+3y+2z=2. If L makes an angles αwith the positive x-axis, then cosα equals
The radius of the circle which touches circle (x+2)2+(y−3)2=25 at point (1,−1) and passes through (4,0) is (a) 4 (b) 5 (c) 3 (d) 8
A line with positive direction cosines passes through the point P(2,–1,2) and makes equal angles with thecoordinate axes. The line meets the plane 2x+y+z=9 at point Q. The length of the line segment PQequals
Write the vector equation of the line passing through (1,2,3) and perpendicular to the plane ri^+2j^−5k^˙+9=0.
If a line makes an angle of 4πwith the positive directions of each of x-axis and y-axis, then the angle that the line makes with the positive direction of the z-axis is
A plane parallel to y-axis passing through line of intersection of planes x+y+z=1 & 2x+3y−z−4=0 which of the point lie on the plane (a) (3,2,1) (b) (−3,0,1) (c) (−3,1,1) (d) (3,−1,1)
if an angle between the line,and the plane,2x−1=1y−2=−2z−3 and the planex−2y−kz=3 is 3cos−1(22)then a value of k is: