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Find the Equation of the Plane Passing Through (A, B, C) and Parallel to the Plane Vecr.(Hati + Hatj + Hatk) = 2 - Mathematics

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प्रश्न

Find the equation of the plane passing through (abc) and parallel to the plane `vecr.(hati + hatj + hatk) = 2`

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उत्तर

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पाठ 11: Three Dimensional Geometry - Exercise 11.4 [पृष्ठ ४९८]

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एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
पाठ 11 Three Dimensional Geometry
Exercise 11.4 | Q 8 | पृष्ठ ४९८

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Find the equations of the planes that passes through three points.

(1, 1, −1), (6, 4, −5), (−4, −2, 3)


Find the equations of the planes that passes through three points.

(1, 1, 0), (1, 2, 1), (−2, 2, −1)


Find the equation of the plane passing through the point (−1, 3, 2) and perpendicular to each of the planes x + 2+ 3z = 5 and 3x + 3z = 0.


If the points (1, 1, p) and (−3, 0, 1) be equidistant from the plane `vecr.(3hati + 4hatj - 12hatk)+ 13 = 0`, then find the value of p.


Find the Cartesian form of the equation of a plane whose vector equation is 

 \[\vec{r} \cdot \left( 12 \hat{i} - 3 \hat{j} + 4 \hat{k} \right) + 5 = 0\]

 


Find the Cartesian form of the equation of a plane whose vector equation is 

  \[\vec{r} \cdot \left( - \hat{i} + \hat{j}  + 2 \hat{k} \right) = 9\]

 


A plane passes through the point (1, −2, 5) and is perpendicular to the line joining the origin to the point

\[ \text{ 3 } \hat{i} + \hat{j} - \hat{k} .\] Find the vector and Cartesian forms of the equation of the plane.

 


Show that the normals to the following pairs of planes are perpendicular to each other.

\[\vec{r} \cdot \left( 2 \hat{i}  - \hat{j}  + 3 \hat{k}  \right) = 5 \text{ and }  \vec{r} \cdot \left( 2 \hat{i}  - 2 \hat{j}  - 2 \hat{k}  \right) = 5\]

find the equation of the plane passing through the point (1, 2, 1) and perpendicular to the line joining the points (1, 4, 2) and (2, 3, 5). Find also the perpendicular distance of the origin from this plane


Find the vector equation of the plane passing through the points (1, 1, −1), (6, 4, −5) and (−4, −2, 3).


Determine the value of λ for which the following planes are perpendicular to each ot

 2x − 4y + 3z = 5 and x + 2y + λz = 5


Find the equation of the plane passing through the points (1, −1, 2) and (2, −2, 2) and which is perpendicular to the plane 6x − 2y + 2z = 9.

 

Find the equation of the plane passing through (abc) and parallel to the plane  \[\vec{r} \cdot \left( \hat{i}  + \hat{j}  + \hat{k}  \right) = 2 .\]

 

Find the equation of the plane passing through (abc) and parallel to the plane \[\vec{r} \cdot \left( \hat{i} + \hat{j} + \hat{k}  \right) = 2 .\]

 

Find the equation of the plane passing through the intersection of the planes x − 2y + z = 1 and 2x + y + z = 8 and parallel to the line with direction ratios proportional to 1, 2, 1. Also, find the perpendicular distance of (1, 1, 1) from this plane


Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the   yz - plane .


Find the coordinates of the point where the line through (3, −4, −5) and (2, −3, 1) crosses the plane 2x + y + z = 7.

 

Find the coordinates of the foot of the perpendicular drawn from the point (5, 4, 2) to the line \[\frac{x + 1}{2} = \frac{y - 3}{3} = \frac{z - 1}{- 1} .\]

 Hence, or otherwise, deduce the length of the perpendicular.

 
 

Find the coordinates of the foot of the perpendicular from the point (1, 1, 2) to the plane 2x − 2y + 4z + 5 = 0. Also, find the length of the perpendicular.

 

Find the coordinates of the foot of the perpendicular from the point (2, 3, 7) to the plane 3x − y − z = 7. Also, find the length of the perpendicular.


Find the length and the foot of the perpendicular from the point (1, 1, 2) to the plane \[\vec{r} \cdot \left( \hat{i}  - 2 \hat{j}  + 4 \hat{k}  \right) + 5 = 0 .\]

 

Find the direction cosines of the unit vector perpendicular to the plane  \[\vec{r} \cdot \left( 6 \hat{i}  - 3 \hat{j} - 2 \hat{k} \right) + 1 = 0\] passing through the origin.

 

Write the equation of a plane which is at a distance of \[5\sqrt{3}\] units from origin and the normal to which is equally inclined to coordinate axes.

 

If the line drawn from (4, −1, 2) meets a plane at right angles at the point (−10, 5, 4), find the equation of the plane.


Find the value of λ for which the following lines are perpendicular to each other `("x"-5)/(5λ+2) = (2 -"y")/(5) = (1 -"z")/(-1); ("x")/(1) = ("y"+1/2)/(2λ) = ("z" -1)/(3)`

hence, find whether the lines intersect or not


The coordinates of the foot of the perpendicular drawn from the point (2, 5, 7) on the x-axis are given by ______.


Prove that the lines x = py + q, z = ry + s and x = p′y + q′, z = r′y + s′ are perpendicular if pp′ + rr′ + 1 = 0.


Find the equation of a plane which bisects perpendicularly the line joining the points A(2, 3, 4) and B(4, 5, 8) at right angles.


Two systems of rectangular axis have the same origin. If a plane cuts them at distances a, b, c and a′, b′, c′, respectively, from the origin, prove that `1/"a"^2 + 1/"b"^2 + 1/"c"^2 = 1/"a'"^2 + 1/"b'"^2 + 1/"c'"^2`


Find the length and the foot of perpendicular from the point `(1, 3/2, 2)` to the plane 2x – 2y + 4z + 5 = 0.


Find the equations of the line passing through the point (3, 0, 1) and parallel to the planes x + 2y = 0 and 3y – z = 0.


The equation of a line, which is parallel to `2hat"i" + hat"j" + 3hat"k"` and which passes through the point (5, –2, 4), is `(x - 5)/2 = (y + 2)/(-1) = (z - 4)/3`.


The point at which the normal to the curve y = `"x" + 1/"x", "x" > 0` is perpendicular to the line 3x – 4y – 7 = 0 is:


The method of splitting a single force into two perpendicular components along x-axis and y-axis is called as ______.


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