Home
Class 12
MATHS
Find the equation of the plane containin...

Find the equation of the plane containing the line `(y)/(b)+(z)/(c)=1,x=0`, and parallel to the line `(x)/(a)-(z)/(c)1,y=0`.

Text Solution

Verified by Experts

The correct Answer is:
`(x)/(a)-(y)/(b)-(z)/(c )+1=0`
The equation of the first line may be written as
`(y)/(b)-(1)/(2)=(1)/(2)-(z)/(c),x=0`
or `(x)/(0)=(y-(1)/(2)b)/(b)=(z-(1)/(2)c)/(-c)" ".....(i)`
Similarly, the equation of the second line may be written as
`(x-(1)/(2)a)/(a)=(y)/(0)=(z+(1)/(2)c)/(c)" ".....(ii)`
The equation of any plane passing through line (i) is
`A(x)+B(y-(1)/(2)b)+C(z-(1)/(2)c)=0" "....(iii)`
where `A.0+B.b-C.c=0" ".....(iv)`
Now plane (iii) will be parallel to line (ii) if
`A.a+B.b-C.c=0" ".....(v)`
Solving (iv) adn (v), we have `(A)/(bc)=(B)/(-ca)=(C)/(-ab)`
Putting these values of A, B and C in (iii), the equation of the required plane is
`bcx-ca(y-(1)/(2)b)=ab(z-(1)/(2)c)=0`
or `(x)/(a)-(y)/(b)-(z)/(c)+1=0`
Promotional Banner

Topper's Solved these Questions

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE|Exercise SUBJECTIVE TYPE|1 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Exercise (Single)|86 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Exercise 3.4|5 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|12 Videos

  • TRIGNOMETRIC RATIOS IDENTITIES AND TRIGNOMETRIC EQUATIONS

    CENGAGE|Exercise Question Bank|4 Videos

Similar Questions

Explore conceptually related problems

Find the Vector and Cartesian equation of the plane containing the line (x-2)/2=(y-2)/3=(z-1)/3 and parallel to the line (x+1)/3=(y-1)/2=(z+1)/1

Find the equation of the plane through the points (1,0,-1),(3,2,2) and parallel to the line (x-1)/1=(y-1)/(-2)=(z-2)/3 .

Find the equation of the plane containing the lines (x-5)/4=(y-7)/4=(z+3)/(-5)a n d(x-8)/7=(y-4)/1=(z-5)/3dot

Find the equation of the plane passing through the points (1,0,-1)a n d(3,2,2) and parallel to the line x-1=(1-y)/2=(z-2)/3dot

Let the equation of the plane containing the line x-y - z -4=0=x+y+ 2z-4 and is parallel to the line of intersection of the planes 2x + 3y +z=1 and x + 3y + 2z = 2 be x + Ay + Bz + C=0 Compute the value of |A+B+C| .

Find the equation of the plane containing the lines 2x-y+z-3=0,3x+y+z=5 and a t a distance of 1/sqrt6 from the point (2,1,-1).

Find the vector and cartesian equations of the plane passing through the points A(1, -2, 3) and B(-1,2,-1) and is parallel to the line (x-2)/(2)=(y+1)/(3)=(z-1)/(4) .

Find the equation of the plane passing through the straight line (x-1)/2=(y+2)/(-3)=z/5 and perpendicular to the plane x-y+z+2=0.

Find ten equation of the plane passing through the point (0,7,-7) and containing the line (x+1)/(-3)=(y-3)/2=(z+2)/1 .

Find the equation of the projection of the line (x-1)/2=(y+1)/(-1)=(z-3)/4 on the plane x+2y+z=9.