मराठी

Find the Intercepts Cut off by the Plane 2x + Y – Z = 5. - Mathematics

Advertisements
Advertisements

प्रश्न

Find the intercepts cut off by the plane 2x + y – z = 5.

Find the sum of the intercepts cut off by the plane \[2x + y - z = 5,\]on the coordinate axes.

 

उत्तर

2x + y – z = 5  ...(1)

Dividing both sides of equation (1) by 5, we obtain

Thus, the intercepts cut off by the plane are `5/2, 5 and -5`

∴ Required sum of intercepts = \[\frac{5}{2} + 5 + \left( - 5 \right) = \frac{5}{2}\] .

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 11: Three Dimensional Geometry - Exercise 11.3 [पृष्ठ ४९३]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 12
पाठ 11 Three Dimensional Geometry
Exercise 11.3 | Q 7 | पृष्ठ ४९३

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Write the sum of intercepts cut off by the plane `vecr.(2hati+hatj-k)-5=0` on the three axes

 


Prove that if a plane has the intercepts abc and is at a distance of P units from the origin, then `1/a^2 + 1/b^2 + 1/c^2 = 1/p^2`


A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A, B, C. Show that the locus of the centroid of triangle ABC is `1/x^2 + 1/y^2 + 1/z^2 = 1/p^2`


if z = x + iy, `w = (2 -iz)/(2z - i)` and |w| = 1. Find the locus of z and illustrate it in the Argand Plane.


Write the equation of the plane whose intercepts on the coordinate axes are 2, −3 and 4.

 

Reduce the equations of the following planes to intercept form and find the intercepts on the coordinate axes. 

 2x + 3y − z = 6


Reduce the equations of the following planes to intercept form and find the intercepts on the coordinate axes. 

2x − y + z = 5

 

 


Find the equation of the plane passing through the point (2, 4, 6) and making equal intercepts on the coordinate axes.


Find the equation of the plane with intercept 3 on the y-axis and parallel to the ZOX plane.

 

Find the equation of the plane through the point \[2 \hat{i}  + \hat{j} - \hat{k} \] and passing through the line of intersection of the planes \[\vec{r} \cdot \left( \hat{i} + 3 \hat{j} - \hat{k}  \right) = 0 \text{ and }  \vec{r} \cdot \left( \hat{j} + 2 \hat{k}  \right) = 0 .\]

 

Find the equation of the plane passing through the line of intersection of the planes 2x − y = 0 and 3z − y = 0 and perpendicular to the plane 4x + 5y − 3z = 8


Find the equation of the plane through the line of intersection of the planes x + 2y + 3z + 4 = 0 and x − y + z + 3 = 0 and passing through the origin.

 

Find the vector equation (in scalar product form) of the plane containing the line of intersection of the planes x − 3y + 2z − 5 = 0 and 2x − y + 3z − 1 = 0 and passing through (1, −2, 3).


Find the equation of the plane that is perpendicular to the plane 5x + 3y + 6z + 8 = 0 and which contains the line of intersection of the planes x + 2y + 3z − 4 = 0, 2x + y − z + 5 = 0.

 

Find the equation of the plane passing through the intersection of the planes 2x + 3y − z+ 1 = 0 and x + y − 2z + 3 = 0 and perpendicular to the plane 3x − y − 2z − 4 = 0.

 

Find the equation of the plane through the line of intersection of the planes  \[\vec{r} \cdot \left( \hat{i} + 3 \hat{j} \right) + 6 = 0  \text{ and } \vec{r} \cdot \left( 3 \hat{i} - \hat{j}  - 4 \hat{k}  \right) = 0,\] which is at a unit distance from the origin.

 

Find the equation of the plane that contains the line of intersection of the planes  \[\vec{r} \cdot \left( \hat{i}  + 2 \hat{j}  + 3 \hat{k}  \right) - 4 = 0 \text{ and }  \vec{r} \cdot \left( 2 \hat{i}  + \hat{j} - \hat{k}  \right) + 5 = 0\] and which is perpendicular  to the plane \[\vec{r} \cdot \left( 5 \hat{i}  + 3 \hat{j}  - 6 \hat{k}  \right) + 8 = 0 .\]

  

Find the equation of the plane passing through the intersection of the planes  \[\vec{r} \cdot \left( 2 \hat{i} + \hat{j}  + 3 \hat{k}  \right) = 7, \vec{r} \cdot \left( 2 \hat{i}  + 5 \hat{j} + 3 \hat{k}  \right) = 9\] and the point (2, 1, 3).

 

A plane makes intercepts −6, 3, 4 respectively on the coordinate axes. Find the length of the perpendicular from the origin on it.


Find the equation of the plane through the intersection of the planes 3x − y + 2z = 4 and x + y + z = 2 and the point (2, 2, 1).


Find the vector equation of the plane passing through the intersection of the planes

\[\vec{r} \cdot \left( \hat{ i } + \hat{ j }+ \hat{ k }\right) = \text{ 6 and }\vec{r} \cdot \left( \text{ 2  } \hat{ i} +\text{  3 } \hat{  j } + \text{ 4 } \hat{ k } \right) = - 5\] and the point (1, 1, 1).


Find the equation of the plane which contains the line of intersection of the planes x \[+\]  2y \[+\]  3 \[z   - \]  4 \[=\]  0 and 2 \[x + y - z\] \[+\] 5  \[=\] 0 and whose x-intercept is twice its z-intercept. Hence, write the equation of the plane passing through the point (2, 3,  \[-\] 1) and parallel to the plane obtained above.


Find the locus of a complex number, z = x + iy, satisfying the relation `|[ z -3i}/{z +3i]| ≤ sqrt2 `. Illustrate the locus of z in the Argand plane.


Find the length of the intercept, cut off by the plane 2x + y − z = 5 on the x-axis

A plane passes through the points (2, 0, 0) (0, 3, 0) and (0, 0, 4). The equation of plane is ______.


The equation of the plane which is parallel to 2x − 3y + z = 0 and which passes through (1, −1, 2) is:


The intercepts made on the coordinate axes by the plane 2x + y − 2z = 3 are:


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×