The plane lx+my=0 is rotated about its l...

The plane `lx+my=0` is rotated about its line of intersection with the plane z=0 through angle measure alpha. Prove that the equation of the plane in new position is `lx+mypmzsqrt(l^2+m^2)tanalpha=0`

Topper's Solved these Questions

RELATION AND FUNCTION INVERSE TRIGONOMETRIC FUNCTIONS LINEAR PROGRAMMING
USHA PUBLICATION|Exercise EXERCISE|103 Videos

Similar Questions

Explore conceptually related problems

The plane 4x+7y+4z+81=0 is rotated through a right angle about its line of intersection with the plane 5x+3y+10z-25=0 . Find the equation of the plane in new position.

Write the equation of the plane perpendicular to y-axis at the point (0,-2, 0).

Write the equation of the plane through origin and passing through the intersection of the planes 3x-2y+z-1=0 and x-2y+3z-1=0

Find the equation of the plane through the points (1,1,0), (-2,2,1) and (1,2,1).

Write the equation of the plane passing through the point(1,0,0),(0,2,0)and (0,0,3).

To which coordinate axis is the plane 2y – 5z=0 parallel ?

To which coordinate axis is the plane 2x+ 3z = 0 parallel ?

USHA PUBLICATION-VECTORS THREE DIMENSIONAL GEOMETRY -EXERCISE

Prove the following by vector method. Median to the base of an isoscel...
Text Solution
|
Prove the following by vector method. In a triangle AOB, mangleAOB = 9...
Text Solution
|
show that the direction of cosines of a vector equally inclined to the...
Text Solution
|
If veca=vecb+vecc, then write the value of veca*(vecbxxvecc).
Text Solution
|
If D is the mid point of side BC of a triangleABC, show by vector meth...
Text Solution
|
Find the scalar components of a unit vector which is perpendicular to ...
Text Solution
|
Decompose the vector 6hati-3hatj-6hatk into vectors which are parallel...
Text Solution
|
Express 2hati-hatj+3hatk as the sum of a vector parallel, and a vector...
Text Solution
|
Resolve the vector vec(b) = hat(i) + hat(j) + hat(k) into vectors para...
Text Solution
|
Find the angle between the following pair of the planes.2x+y+2z-4=0and...
Text Solution
|
Show that the join of the points (6,-4,4) and (0,0,-4) intersects the ...
Text Solution
|
Show that the points (2,3,-5) and (3,4,7) lie on the opposite side of ...
Text Solution
|
Find dy/dx if y=log(sec x+tan x).
Text Solution
|
Obtain the equation of the line through the point (1, 2, -3) and perpe...
Text Solution
|
Find the shortest distance between the lines frac[x][2]=frac[y][-3]=fr...
Text Solution
|
Find the equation of the plane passing through the line frac[x+1][-3]=...
Text Solution
|
Find the equation of the plane containing the line frac[x+3][3]=frac[y...
Text Solution
|
Show that lines vecr = (hat(i) + hat(j) - hat(k)) + lambda(3hat(i) - h...
Text Solution
|
If P is the point (2,1,6), then find the point Q such that PQ is perpe...
Text Solution
|
The plane lx+my=0 is rotated about its line of intersection with the p...
Text Solution
|