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(A) Find the equation of the plane throu...

(A) Find the equation of the plane through the intersection of the plane :
3x - y + 2z - 4 = 0 and x + y + z - 2 = 0
and the point (2,2,1).
(b) Find the vector equation of the plane through the intersection of the planes :
`vec(r) . (hati + hatj + hatk) = 6 " and " vec(r). (2 hati + 3 hatj + 4 hatk) = - 5 ` at the point. (1,1,1).

Text Solution

Verified by Experts

The correct Answer is:
`vec(r). (20 hati + 23 hatj + 26 hatk) = 69`.
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Knowledge Check

  • Find the vector equation of a plane passing through the intersection of the planes vecr.(hati+hatj+hatk) = 6 and vecr. (2hati+3hatj+4hatk) - 5 = 0 and through the point (2,2,1) .

    A
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    B
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  • The equation of the plane through the line of intersection of the planes x + y + z - 1 = 0 and 2x + y - 3z + 2 = 0 passing through the point (1,1,1), is

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    D
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  • The equation of the plane through the intersection of the planes 3x-y+2z-4=0, x+y+z-2=0 and the point (2,2,1) is

    A
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    B
    `7x+5y+4z-8=0`
    C
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    D
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