Let L be the line of intersection of t...

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 a.`1/(sqrt(3))` b. `1/2` c. 1 d.`1/(sqrt(2))`

Topper's Solved these Questions

THEORY OF EQUATIONS
CENGAGE ENGLISH|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos
THREE-DIMENSIONAL GEOMETRY
CENGAGE ENGLISH|Exercise ARCHIVES INTEGER TYPE|1 Videos

Similar Questions

Explore conceptually related problems

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 1/(sqrt(3)) 1/2 1 1/(sqrt(2))

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

If the plane 2x-3y+6z=11 makes an angle sin^(-1) (alpha) with the x-axis , then the value of alpha is

The equation of the plane through the intersection of the planes x+y+z=1 and 2x+3y-z+4 = 0 and parallel to x-axis is

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 makes an angle theta with the x-axis and the y-axis. If it makes an angle alpha with the z - axis such that sin^(2)alpha= 3sin^(2)theta , then cos ^(2)theta is equal to

The equation of a plane passing through the line of intersection of the planes x+2y+3z = 2 and x - y + z = 3 and at a distance 2/sqrt 3 from the point (3, 1, -1) is

The equation of the plane passing through the line of intersection of the planes x+y+z+3 =0 and 2x-y + 3z +2 =0 and parallel to the line (x)/(1) = (y)/(2) = (z)/(3) is

Let the equation of a line through (3, 6, -2) and parallel to the planes x-y+2z=5 and 3x+y+2z=6 is L=0 . If point (alpha,beta, 2) satisfy L=0 , then alpha+2beta is equal to

CENGAGE ENGLISH-THREE DIMENSIONAL GEOMETRY-All Questions

A variable plane passes through a fixed point (alpha,beta,gamma) an...
Text Solution
|
Show that the straight lines whose direction cosines are given by the ...
Text Solution
|
The perpendicular distance of a corner of uni cube from a diagonal not...
Text Solution
|
If the direction cosines of a variable line in two adjacent points be ...
Text Solution
|
the image of the point (-1,3,4) in the plane x-2y=0 a.(-(17)/(3),(19)/...
Text Solution
|
The ratio in which the plane vec rdot (vec i-2 vec j+3 vec k )=17 d...
Text Solution
|
Let L be the line of intersection of the planes 2x""+""3y""+""z""=""...
Text Solution
|
The distance between the line vec r=2 hat i-2 hat j+3 hat k+lambda...
Text Solution
|
If angle theta bertween the line (x+1)/1=(y-1)/2=(z-2)/2 and the plane...
Text Solution
|
The length of the perpendicular drawn from (1,2,3) to the line (x-6...
Text Solution
|
A plane makes intercepts O A ,O Ba n dO C whose measurements are a,b ...
Text Solution
|
The intersection of the spheres x^2+y^2+z^2+7x-2y-z=13a n dx^2+y^2+...
Text Solution
|
The shortest distance from the plane 12 x+4y+3z=327 to the sphere ...
Text Solution
|
A line makes an angel theta with each of the x-and z-axes. If the ...
Text Solution
|
Find the equation of a straight line in the plane vec r* vec n=d ...
Text Solution
|
What is the nature of the intersection of the set of planes x+a y+(b...
Text Solution
|
Let P1 denote the equation of a plane to which the vector ( hat i+...
Text Solution
|
Let P M be the perpendicular from the point P(1,2,3) to the x-y pla...
Text Solution
|
If the plane x/2+y/3+z/6=1 cuts the axes of coordinates at points, A ,...
Text Solution
|
For what value (s) of a will the two points (1,a,1) and (-3,0,a) lie ...
Text Solution
|