Find the equation of the plane which passes through the point 2- -3- -k- and perpendicular to the vector 3- -2- -2k- Also find the perpendicular distance of this plane from the origin-

Assume that the equation of normal to plane is n⃗=aî+bĵ+ck̂ and the point on plane is of form p⃗=x_0î+y_0ĵ+z_0k̂ Hence, equation of plane with normal ...

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Standard XII

Mathematics

Direction Cosines

Find the equa...

Question

Find the equation of the plane which passes through the point $2^i + 3^j -^k$ and perpendicular to the vector $3^i - 2^j - 2^k$ . Also find the perpendicular distance of this plane from the origin.

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Solution

Assume that the equation of normal to plane is $\to n = a^i + b^j + c^k$ and the point on plane is of form $\to p = x_{0}^i + y_{0}^j + z_{0}^k$
Hence, equation of plane with normal $\to n$ and passing through point $\to p$ is $a (x - x_{0}) + b (y - y_{0}) + c (z - z_{0}) = 0$
$∴ 3 (x - 2) - 2 (y - 3) - 2 (z + 1) = 0$
$∴ 3 x - 2 y - 2 z = 2$
This is the required equation of plane.

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Similar questions

Q. Find the vector equation of the plane passing through a point having position vector

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and perpendicular to the vector

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and

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\to r = 3^i -^j -^k + λ (2^i - 2^j +^k)

Q. Find the equation of the plane perpendicular to vector

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and passing through the point

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Q. Unit vector perpendicular to the plane passing through the points

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and

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& perpendicular to the line of intersection of the planes

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and

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Find the equation of the plane which passes through the point 2^i+3^j−^k and perpendicular to the vector 3^i−2^j−2^k. Also find the perpendicular distance of this plane from the origin.

Find the equation of the plane which passes through the point $2^i + 3^j -^k$ and perpendicular to the vector $3^i - 2^j - 2^k$ . Also find the perpendicular distance of this plane from the origin.