मराठी

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

Advertisements
Advertisements

प्रश्न

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

पर्याय

  • (2, 0, 0)

  • (0, 5, 0)

  • (0, 0, 7)

  • (0, 5, 7)

MCQ
रिकाम्या जागा भरा
Advertisements

उत्तर

The coordinates of the foot of the perpendicular drawn from the point (2, 5, 7) on the x-axis are given by (2, 0, 0).

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 11: Three Dimensional Geometry - Solved Examples [पृष्ठ २३२]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 11 Three Dimensional Geometry
Solved Examples | Q 14 | पृष्ठ २३२

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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 vector equation of each one of following planes. 

x + y − z = 5

 


Find the vector equation of each one of following planes. 

x + y = 3

 

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.

 


Find the equation of the plane that bisects the line segment joining the points (1, 2, 3) and (3, 4, 5) and is at right angle to it.

 

Find the vector equation of a plane which is at a distance of 5 units from the origin and which is normal to the vector  \[\hat{i}  - \text{2 } \hat{j}  -  \text{2 } \hat{k} .\]

 


Find the vector equation of the plane passing through the points (1, 1, 1), (1, −1, 1) and (−7, −3, −5).


Find the vector equation of the plane passing through the points \[3 \hat{i}  + 4 \hat{j}  + 2 \hat{k} , 2 \hat{i} - 2 \hat{j} - \hat{k}  \text{ and }  7 \hat{i}  + 6 \hat{k}  .\]

 

Obtain the equation of the plane passing through the point (1, −3, −2) and perpendicular to the planes x + 2y + 2z = 5 and 3x + 3y + 2z = 8.

 

Find the equation of the plane passing through the origin and perpendicular to each of the planes x + 2y − z = 1 and 3x − 4y + z = 5.

 

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 point (−1, 3, 2) and perpendicular to each of the planes x + 2y + 3z = 5 and 3x + 3y + z = 0.

 

Find the vector equation of the plane through the points (2, 1, −1) and (−1, 3, 4) and perpendicular to the plane x − 2y + 4z = 10 


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 through (2, 3, −4) and (1, −1, 3) and parallel to x-axis.

 

Find the equation of the plane through the points (2, 2, −1) and (3, 4, 2) and parallel to the line whose direction ratios are 7, 0, 6.

 

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane \[\vec{r} \cdot \left( \hat{i}  + 2 \hat{j}  - 5 \hat{k}  \right) + 9 = 0 .\]

 

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


Find the equation of a plane which passes through the point (3, 2, 0) and contains the line  \[\frac{x - 3}{1} = \frac{y - 6}{5} = \frac{z - 4}{4}\] .

 


Find the image of the point (0, 0, 0) in the plane 3x + 4y − 6z + 1 = 0.

 

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 length and the foot of perpendicular from the point \[\left( 1, \frac{3}{2}, 2 \right)\]  to the plane \[2x - 2y + 4z + 5 = 0\] .

 

Find the position vector of the foot of perpendicular and the perpendicular distance from the point P with position vector \[2 \hat{i}  + 3 \hat{j}  + 4 \hat{k} \] to the plane  \[\vec{r} . \left( 2 \hat{i} + \hat{j}  + 3 \hat{k}  \right) - 26 = 0\] Also find image of P in the plane.

 

Write the intercepts made by the plane 2x − 3y + 4z = 12 on the coordinate axes.

 

Find the length of the perpendicular drawn from the origin to the plane 2x − 3y + 6z + 21 = 0.

 

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 equation of the plane which bisects the line segment joining the points (−1, 2, 3) and (3, −5, 6) at right angles.


Find the coordinates of the foot of the perpendicular Q  drawn from P(3, 2, 1) to the plane 2x − y + z + 1 = 0. Also, find the distance PQ and the image of the point P treating this plane as a mirror

Find the image of the point (1, 6, 3) in the line `x/1 = (y - 1)/2 = (z - 2)/3`.


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.


Show that the points `(hat"i" - hat"j" + 3hat"k")` and `3(hat"i" + hat"j" + hat"k")` are equidistant from the plane `vec"r" * (5hat"i" + 2hat"j" - 7hat"k") + 9` = 0 and lies on opposite side of it.


If the foot of perpendicular drawn from the origin to a plane is (5, – 3, – 2), then the equation of plane is `vec"r".(5hat"i" - 3hat"j" - 2hat"k")` = 38.


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


A unit vector perpendicular to the plane ABC, where A, B and C are respectively the points (3, –1, 2), (1, –1, –3) and (4, –3, 1), is


The coordinates of the foot of the perpendicular drawn from the point A(1, 0, 3) to the join of the points B(4, 7, 1) and C(3, 5, 3) are


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×