A plane which bisects the angle between the two given planes `2x-y+2z-4=0" and "x+2y+2z-2=0`, passes through the pointA. (1, -4, 1)B. (1, 4, -1)C. (2, 4, 1)D. (2, -4, 1)

A plane which bisects the angle between the two given planes `2x-y+2z-

1.	A plane which bisects the angle between the two given planes `2x-y+2z-4=0" and "x+2y+2z-2=0`, passes through the pointA. (1, -4, 1)B. (1, 4, -1)C. (2, 4, 1)D. (2, -4, 1)
Answer» Correct Answer - D Equation of planes bisecting the angles between the planes `a_(1)x+b_(1)y+c_(1)z+d_(1)=0" and"` `a_(2)x+b_(2)y+c_(2)z+d_(2)=0," and"` `(a_(1)x+b_(1)y+c_(1)z+d_(1))/(sqrt(a_(1)^(2)+b_(1)^(2)+c_(1)^(2)))=+-(a_(2)x+b_(2)y+c_(2)z+d_(2))/(sqrt(a_(2)^(2)+b_(2)^(2)+c_(2)^(2)))` Equation of given planes are `2x-y+2z-4=0" "...(i)` and `" "z+2y+2z-2=0" "...(ii)` Now, equation of planes bisecting the angles between the planes (i) and (ii) are `(2x-y+2z-4)/(sqrt(4-1-4))=+-(x+2y+2z-2)/(sqrt(1+4+4))` `implies" "2x-y+2z-4=+-(x+2y+2z-2)` On taking (+ve) sign, we get a plane `x-3y=2" "...(iii)` On taking(-ve)sing, we get a plane `3x+y+4z=6" "...(iv)` Now from the given options, the point (2, -4, 1) satisfy the plane of angle bisector `3x+y+4z=6`

Discussion

No Comment Found

Related InterviewSolutions

Read the following passage and answer the questions. Consider the lines `L_(1):(x+1)/(3)=(y+2)/(1)=(z+1)/(2),L_(2):(x-2)/(1)=(y+2)/(2)=(z-3)/(3)` The distance of the point (1,1,1) from the plane passing throught the point (-1,-2,-1) and whose normal is perpendicular to both the lines `L_(1)` and `L_(2)`, isA. `2//sqrt(75)` unitB. `7//sqrt(75)` unitsC. `13//sqrt(75)` unitsD. `23//sqrt(75)` units
Read the following passage and answer the questions. Consider the lines `L_(1):(x+1)/(3)=(y+2)/(1)=(z+1)/(2),L_(2):(x-2)/(1)=(y+2)/(2)=(z-3)/(3)` The unit vector perpendicualr to both `L_(1)` and `L_(2)` isA. `(-hati+7hatj+7hatk)/(sqrt(99))`B. `(-hati-7hatj+5hatk)/(5sqrt(3))`C. `(-hati+7hatj+5hatk)/(5sqrt(3))`D. `(7hati-7hatj-hatk)/(sqrt(99))`
Consider the line L 1 : x 1 y 2 z 1 312 +++ ==, L2 : x2y2z3 123A. 0 unitB. `17//sqrt(3)` unitsC. `41//sqrt(5)`D. `17//5sqrt(3)` units
If the distance between the plane Ax 2y + z = d and the plane containing the lines2 1x=3 2y=4 3zand3 2x=4 3y=5 4zis 6 , then |d| is
The angle betweenthe lines whose direction cosines satisfy the equations `l+m+n=""0`and `l^2=m^2+n^2`is(1) `pi/3`(2) `pi/4`(3) `pi/6`(4) `pi/2`A. `(pi)/(3)`B. `(pi)/(4)`C. `(pi)/(6)`D. `(pi)/(2)`
The distance of the point `(1,-5,""9)`from the plane `x-y+z=5`measured along the line `x=y=z`is :(1) `3sqrt(10)`(2) `10sqrt(3)`(3) `(10)/(sqrt(3))`(4) `(20)/3`A. `3sqrt(10)`B. `10sqrt(3)`C. `(10)/(sqrt(3))`D. `(20)/(3)`
Equation of the plane containing the straight line `x/2=y/3=z/4` and perpendicular to the plane containing the straight lines `x/2=y/4=z/2` and `x/4=y/2=z/3` isA. `5x+2y-4z=0`B. `x+2y-2z=0`C. `ax+2y-3z=0`D. `x-2y+z=0`
If `L_1` is the line of intersection of the planes `2x-2y+3x-2=0``x-y+z+1=0` and `L_2` is the line of the intersection of the planes `x+2y-z-3=0` `3x-y+2z-1=0`then the distance of the origin from the plane containing the lines `L_1` and `L_2` isA. `(1)/(4sqrt(2))`B. `(1)/(3sqrt(2))`C. `(1)/(2sqrt(2))`D. `(1)/(sqrt(2))`
The length of the perpendicular drawn from the point (2, 1, 4) to the plane containing the lines `r=(hati+hatj)+lambda(hati+2hatj-hatk)" and "r=(hati+hatj)+mu(-hati+hatj-2hatk)` isA. 3B. `(1)/(3)`C. `sqrt(3)`D. `(1)/(sqrt(3))`
Thedistance of the point (1, 0, 2) from the point of intersection of the line `(x-2)/3=(y+1)/4=(z-2)/(12)`and the plane x y + z = 16, is :(1) `2sqrt(14)`(2) 8 (3) `3sqrt(21)`(4) 27A. `2sqrt(14)`B. 8C. `3sqrt(21)`D. 13

A plane which bisects the angle between the two given planes `2x-y+2z-4=0" and "x+2y+2z-2=0`, passes through the pointA. (1, -4, 1)B. (1, 4, -1)C. (2, 4, 1)D. (2, -4, 1)

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment