Grade 12th passAnalytical Geometry
Find the equation of the plane which bisects the angle between the planes3x-4y+12z=26 and x+2y-2z=9
1 Answer
Vikas TU
Dear Student,
ATQ given eqns are 3x-4y+12z-26=0 and x+2y-2z-9=0
plane bisector of angles between them:
(3x-4y+12z-26)/sqrt(9+16+144) = (x+2y-2z-9)/sqrt(1+4+4)
=>3(3x-4y+12z-26)= 13(x+2y-2z-9)
=>4x+38y-62z-39=0 and 22x+14y+10z-195=0
theta be the angle between the second plane and 2x+14y+10z-195=0:
cos theta =sqrt(5/39) (putting formula for cos theta)
sin theta= sqrt(34/39)
so tan theta=sqrt(34/5) >1 or theta >45 degrees.
so 2x+14y+10z-195=0 is obtuse angle bisector and 4x+38y-62z-39=0 is acute angle bisector. [Ans]
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)
Thapar University)
Other Related Questions on analytical geometry
- The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is
- The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is
analytical geometry
Last Activity: 4 Years ago
show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)
show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)
analytical geometry
Last Activity: 4 Years ago
show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0
show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0
analytical geometry
Last Activity: 4 Years ago
A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius.
A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius.
analytical geometry
Last Activity: 4 Years ago
Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d
Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d
analytical geometry
Last Activity: 4 Years ago