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Find the vector and cartesian equation of plane which is at a distance 5 units from the origin and having a normal vector `3hati+2hatj-hatk`.

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Find the vector and cartesian equation of a plane which is at a distance of 3 units from the origin and which is normal to the vector veci+2hatj-2hatk .

Find the vector and cartesian equations of a plane which is at a distance of 18 units from the origin and which is normal to the vector 2veci+7vecj+8veck .

Knowledge Check

  • The vector equation of a plane which is at a distance of 6/sqrt29 from the origin and its normal vector from the origin is 2hati-3hatj+4hatk is

    A
    `vecr.(2hati-3hatj+4hatk)=6/sqrt29`
    B
    `vecr.(2/sqrt29 hati-3/sqrt29 hatj+4/sqrt29hatk)=6/sqrt29`
    C
    both (a) and (b)
    D
    none of these

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    Find the vector equation of the plane which is at a distance of 6/sqrt29 from the origin and its normal vector from the origin is 2hati-3hatj+4hatk . Also find its cartesian form.

    Find a parametric form of vector equation of a plane which is at a distance of 7 units from the origin having 3,-4,5 as direction ratios of a normal to it.

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    Find the vector and cartesian equations of the planes a. that passes through the point (1,0,-2) and normal to the planes is hati+hatj-hatk b. that passes through the point (1,4,6) and the normal vector to the plane is hati-2hatj+hatk .

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