Let L be the line of intersection of the planes `2x""+""3y""+""z""=""1` and `x""+""3y""+""2z""=""2` . If L makes an angles ` alpha ` with the positive x-axis, then cos` alpha ` equals

The equation of the plane through the line of intersection of the planes 2x+y-z+5=0 and x+2y+3z=4 and perpendicular to the plane 5x+3y+6z=10 is -

Consider three planes P_1 : x-y + z = 1 , P_2 : x + y-z=-1 and P_3 : x-3y + 3z = 2 Let L_1, L_2 and L_3 be the lines of intersection of the planes P_2 and P_3 , P_3 and P_1 and P_1 and P_2 respectively. Statement 1: At least two of the lines L_1, L_2 and L_3 are non-parallel . Statement 2:The three planes do not have a common point

Find the angle between the lines 2x=3y=-z and 6x=-y=-4z

Find the angle between the planes 2x+y-2z+3=0a n d 6x−2y+3z=5

a straight line makes an angle 45^@ with positive direction of x-axis and 60^@ with positive direction of z-axis. If the line makes and angle theta with positive direction of y-axis then theta is equal to-

Statement -I : A line makes the same angle theta with each of the x and z-axis. If it makes an angle alpha with the y-axis, such that sin^(2) alpha=3 sin^(2) theta , then cos^(2) theta=3/5 . Statement -II : If a line with direction ratios, l, m, n makes angles alpha, beta, gamma respectively with x, y amd z-axis then cos alpha=(l)/sqrt(l^(2)+m^(2)+n^(2)), cos beta =(m)/sqrt(l^(2)+m^(2)+n^(2)) and cos gamma =(n)/sqrt(l^(2)+m^(2)+n^(2)) .

Let the equation of the plane containing the line x-y - z -4=0=x+y+ 2z-4 and is parallel to the line of intersection of the planes 2x + 3y +z=1 and x + 3y + 2z = 2 be x + Ay + Bz + C=0 Compute the value of |A+B+C| .

The actue angle between the plane 2x-y+z=6 and x+y+2z=3 is __

Find the equation of the staight line passing through the point of intersection of the straight lines 2x+3y+4=0 and 3x+y-1=0 and inclined to the positive direction of the x - axis at an angle 135^(@) .

Find the equation of the plane passing through the intersection of the planes 2x+y+2z=9" and " 4x-5y-4z=1 and through the point (3,2,-1).