A variable line passing through the point P(0, 0, 2) always makes angle `60^(@)` with z-axis, intersects the plane `x+y+z=1`. Find the locus of point of intersection of the line and the plane.

A Straight line drawn through the point A(2,1) making an angle pi//4 with positive x-axis intersects another line x+2y+1=0 in the point Bdot Find length A B .

Find the points of intersection of the line (x-2)/(-3)=(y-1)/2=(z-3)/2 and the plane 2x+y-z=3 .

A line is drawn from the point P(1,1,1)and perpendicular to a line with direction ratios, (1,1,1) to intersect the plane x+2y+3z=4 at Q. The locus of point Q is

A plane passes through the point (0,-1,0) and (0,0,1) and makes an angle of (pi)/(4) with the plane y-z=0 then the point which satisfies the desired plane is

Find the equation of line of intersection of the planes 3x-y+ z=1 and x + 4 y -2 z =2.

Two straight lines having variable slopes m_(1) and m_(2) pass through the fixed points (a, 0) and (-a, 0) respectively. If m_(1)m_(2)=2 , then the eccentricity of the locus of the point of intersection of the lines is

The straight line passing through P(x_1,y_1) and making an angle alpha with x-axis intersects Ax + By + C=0 in Q then PQ =________________

Find the ratio in which the plane 2x-3y+z=8 divides the line segment joining the points A(3, -2,1) and B(1, 4, -3). Also find the point of intersection of the line and the plane.

Find the coordinates of the point, where the line (x-2)/3=(y+1)/4=(z-2)/2 intersects the plane x-y+z-5=0 . Also find the angle between the line and the plane.

Find the coordinates of the point, where the line (x-2)/3=(y+1)/4=(z-2)/2 intersects the plane x-y+z-5=0 . Also find the angle between the line and the plane.