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Find the equations of the planes passing...

Find the equations of the planes passing through the line of intersection of the planes `vecr.(hati + 3hatj) = 6` and `vecr.(3hati - hatj-4hatk)=0`, which are at a distance of 1 unit from the origin.

Answer

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Find the Cartesian and vector equation of the planes through the line of intersection of the planes vecr.(hati-hatj)+6=0 and vecr.(3hati+3hatj-4hatk)=0 , which are at a unit distance from the origin.

Find the equation of the plane passing through the line of intersection of the planes vecr.(hati+3hatj)-6=0 and vecr.(3hati-hatj-4hatk)=0 , whose perpendicular distance from the origin is unity.

Knowledge Check

  • The line of intersection of the planes vecr.(3hati-hatj+hatk)=1 and vecr.(hati+4hatj-2hatk)=2 is parallel is

    A
    `2hati+7hatj+13hatk`
    B
    `-2hati-7hatj+13hatk`
    C
    `2hati+7hatj-13hatk`
    D
    `-2hati+7hatj+13hatk`

  • The line of intersection of the planes vecr . (3 hati - hatj + hatk) =1 and vecr. (hati+ 4 hatj -2 hatk)=2 is:

    A
    `(x-(4)/(7))/(-2) = y/7=(z- (5)/(7))/(13)`
    B
    `(x-(6)/(13))/(2) = (y- (5)/(13))/(7) = (z)/(-13)`
    C
    `(x - (4)/(7))/(2) = (y)/(-7) (z + (5)/(7))/(13)`
    D
    `(x- (6)/(13))/(2) = (y- (5)/(13))/(-7) = (z)/(-13)`

  • The vector equation of the line of intersection of the planes vecr.(2hati+3hatk)=0 and vecr.(3hati+2hatj+hatk)=0 is

    A
    `vecr=lamda(hati+2hatj+hatk)`
    B
    `vecr=lamda(hati-2hatj+3hatk)`
    C
    `vecr=lamda(hati+2hatj-3hatk)`
    D
    none of these

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    Find the equation of the plane passing through the line of intersection of the planes vecr.(hati+hatj+hatk)=1 and vecr.(2hati+3hatj-hatk)+4=0 and parallel to x-axis.

    Find the Cartesian as well as the vector equation of the planes pasing through the intersection of the planes vecr.(2hati=6hatj)+12=0 and vecr.(3hati-hatj+4hatk)=0 which are at unit distance from the origin.

    Find the equation of the plane passing through the intersection of the planes vecr.(2hati+hatj+3hatk)=7 , vecr.(2hati+5hatj+3hatk)=9 and the point (2,1,3) .

    Find the vector equation of the plane passing through the intersection of the planes vecr.(hati+hatj+hatk)=6, vecr.(2hati+3hatj+4hatk)=-5 and the point (1,1,1) .

    Find the equation of the plane passing through the intersection of the planes vecr.(2hati+hatj+3hatk)=7, vecr.(2hati+5hatj+3hatk)=9 and the point (3,2,-1) .

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