Let `L` be the line of intersection of the planes `2x+3y+z=1a n dx+3y+2z=2.` If `L` makes an angle `alpha` with the positive x-axis, then `cosalpha` equals a. `1/2` b. `1` c. `1/(sqrt(2))` d. `1/(sqrt(3))`

Find the acute angle between the planes 2x-3y+5z=1 and x-y-z=7 .

Find the point intersection of the line x-1=(y)/(2)=z+1" with the plane "2x-y+2z=2. Also, find the angle between the line and the plane.

Let P M be the perpendicular from the point P(1,2,3) to the x-y plane. If vec O P makes an angle theta with the positive direction of the z- axis and vec O M makes an angle phi with the positive direction of x- axis, w h e r eO is the origin and thetaa n dphi are acute angels, then a. costhetacosphi=1//sqrt(14) b. sinthetasinphi=2//sqrt(14) c. ""tanphi=2 d. tantheta=sqrt(5)//3

Let P=0 be the equation of a plane passing through the line of intersection of the planes 2x-y=0a n d3z-y=0 and perpendicular to the plane 4x+5y-3z=8. Then the points which lie on the plane P=0 is/are a. (0,9,17) b. (1//7,21//9) c. (1,3,-4) d. (1//2,1,1//3)

Find the equation of the plane containing the line of intersection of the planes x + y + z - 6 = 0 and 2x + 3y + 4z + 5 = 0 and passing through the point (1,1,1)

Find the equation of the plane through the intersection of the planes 2x - 3y + z - = 0 and x - y + z + 1 = 0 and perpendicular to the plane x + 2y - 3z + 6 = 0.

If the line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the plane 2x+3y-z+13=0 at a point P and the plane 3x+y+4z=16 at a point Q, then PQ is equal to

Find the point of intersection of the lines (x-1)/(3)=(y-1)/(-1) = z+2’and (x-4)/(2)=y=(z+1)/(3) .

Find the equation of the plane through the line of intersection of the planes x+y+z=1 and 2x+3y+4z=5 which is perpendicular to the plane x-y+z=0

The intersection of the planes 2 x-y-3 z=8 and x+2 y-4 z=14 is the line L . The value of a ' for which the line L is perpendicular to the line through (a, 2,2) and (6,11,-1 is