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The equation of the bisector of the angle between two planes a1x + b1y + c1z +d1 = 0 and a2x + b2y + c2z + d2 = 0
containing the origin is given by
provided
containing the origin is given by
provided- a)d1d2=0
- b)d1d2>0
- c)d1d2<0
- d)d1<d2
Correct answer is option 'B'. Can you explain this answer?
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The equation of the bisector of the angle between two planes a1x + b1y...
Equations of planes bisecting the angle between two given planes.
Let the given planes
If (x, y, z) be a point cm any one of the planes bisecting the angles between the planes (i) and (ii), then the perpendiculars from (x,z,x) on the two planes must be equal in magnitude (may be opposite in sign) so that
are the equations of the two bisecting planes.
Remark: 1- Sometimes we are required to find which of the planes bisect the angle between the given planes that contains the origin. To do this, we express the equations of the given planes in the form so that the constant terms in both of them are positive.
bisects that angle between the planes which contains the origin.
Naturally, the other bisecting plane
bisects the angle between the planes that does not contain the origin.
Remark: 2- If a1a2 + b1b2 + c1c2 < 0, then the origin lies in the acute angle and if a1a2 + b1b2 + c1c2 > 0 then the origin lies in the obtuse angle.
Let the given planes
If (x, y, z) be a point cm any one of the planes bisecting the angles between the planes (i) and (ii), then the perpendiculars from (x,z,x) on the two planes must be equal in magnitude (may be opposite in sign) so that
are the equations of the two bisecting planes.
Remark: 1- Sometimes we are required to find which of the planes bisect the angle between the given planes that contains the origin. To do this, we express the equations of the given planes in the form so that the constant terms in both of them are positive.
bisects that angle between the planes which contains the origin.
Naturally, the other bisecting plane
bisects the angle between the planes that does not contain the origin.
Remark: 2- If a1a2 + b1b2 + c1c2 < 0, then the origin lies in the acute angle and if a1a2 + b1b2 + c1c2 > 0 then the origin lies in the obtuse angle.
Most Upvoted Answer
The equation of the bisector of the angle between two planes a1x + b1y...
Equations of planes bisecting the angle between two given planes.
Let the given planes
If (x, y, z) be a point cm any one of the planes bisecting the angles between the planes (i) and (ii), then the perpendiculars from (x,z,x) on the two planes must be equal in magnitude (may be opposite in sign) so that
are the equations of the two bisecting planes.
Remark: 1- Sometimes we are required to find which of the planes bisect the angle between the given planes that contains the origin. To do this, we express the equations of the given planes in the form so that the constant terms in both of them are positive.
bisects that angle between the planes which contains the origin.
Naturally, the other bisecting plane
bisects the angle between the planes that does not contain the origin.
Remark: 2- If a1a2 + b1b2 + c1c2 < 0, then the origin lies in the acute angle and if a1a2 + b1b2 + c1c2 > 0 then the origin lies in the obtuse angle.
Let the given planes
If (x, y, z) be a point cm any one of the planes bisecting the angles between the planes (i) and (ii), then the perpendiculars from (x,z,x) on the two planes must be equal in magnitude (may be opposite in sign) so that
are the equations of the two bisecting planes.
Remark: 1- Sometimes we are required to find which of the planes bisect the angle between the given planes that contains the origin. To do this, we express the equations of the given planes in the form so that the constant terms in both of them are positive.
bisects that angle between the planes which contains the origin.
Naturally, the other bisecting plane
bisects the angle between the planes that does not contain the origin.
Remark: 2- If a1a2 + b1b2 + c1c2 < 0, then the origin lies in the acute angle and if a1a2 + b1b2 + c1c2 > 0 then the origin lies in the obtuse angle.
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The equation of the bisector of the angle between two planes a1x + b1y + c1z +d1= 0 and a2x + b2y+ c2z + d2 = 0containing the origin is given byprovideda)d1d2=0b)d1d2>0c)d1d2<0d)d1<d2Correct answer is option 'B'. Can you explain this answer?
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