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प्रश्न
In the given cases, find the distance of each of the given points from the corresponding given plane.
Point Plane
(– 6, 0, 0) 2x – 3y + 6z – 2 = 0
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उत्तर
It is known that the distance between a point, p(x1, y1, z1), and a plane, Ax + By + Cz = D, is given by,
The given point is (−6, 0, 0) and the plane is 2x – 3y + 6z – 2 = 0
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संबंधित प्रश्न
In the given cases, find the distance of each of the given points from the corresponding given plane.
Point Plane
(2, 3, – 5) x + 2y – 2z = 9
Find the distance of the point (−1, −5, −10) from the point of intersection of the line `vecr = 2hati -hatj + 2hatk + lambda(3hati + 4hatj + 2hatk)` and the plane `vecr.(hati -hatj + hatk) = 5`.
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Find the distance of the point \[2 \hat{i} - \hat{j} - 4 \hat{k}\] from the plane \[\vec{r} \cdot \left( 3 \hat{i} - 4 \hat{j} + 12 \hat{k} \right) - 9 = 0 .\]
Find the distance of the point (2, 3, −5) from the plane x + 2y − 2z − 9 = 0.
Find the equations of the planes parallel to the plane x + 2y − 2z + 8 = 0 that are at a distance of 2 units from the point (2, 1, 1).
Find the distance of the point (2, 3, 5) from the xy - plane.
Find an equation for the set of all points that are equidistant from the planes 3x − 4y + 12z = 6 and 4x + 3z = 7.
Find the distance between the point (7, 2, 4) and the plane determined by the points A(2, 5, −3), B(−2, −3, 5) and C (5, 3, −3).
Find the equation of the plane which passes through the point (3, 4, −1) and is parallel to the plane 2x − 3y + 5z + 7 = 0. Also, find the distance between the two planes.
Find the equation of the plane mid-parallel to the planes 2x − 2y + z + 3 = 0 and 2x − 2y + z + 9 = 0.
Find the distance between the planes \[\vec{r} \cdot \left( \hat{i} + 2 \hat{j} + 3 \hat{k} \right) + 7 = 0 \text{ and } \vec{r} \cdot \left( 2 \hat{i} + 4 \hat{j} + 6 \hat{k} \right) + 7 = 0 .\]
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Find the distance of the point whose position vector is `(2hat"i" + hat"j" - hat"k")` from the plane `vec"r" * (hat"i" - 2hat"j" + 4hat"k")` = 9
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If the points (1, 1, λ) and (–3, 0, 1) are equidistant from the plane `barr*(3hati + 4hatj - 12hatk) + 13` = 0, find the value of λ.
Find the equations of the planes parallel to the plane x – 2y + 2z – 4 = 0 which is a unit distance from the point (1, 2, 3).
In the figure given below, if the coordinates of the point P are (a, b, c), then what are the perpendicular distances of P from XY, YZ and ZX planes respectively?
