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

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

If O be the origin and the coordinates of P be (1, 2, −3), then find the equation of the plane passing through P and perpendicular to OP.


Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes `vecr = (hati - hatj + 2hatk)  = 5`and `vecr.(3hati + hatj + hatk) = 6`


Find the vector equations of the coordinate planes.

 

The coordinates of the foot of the perpendicular drawn from the origin to a plane are (12, −4, 3). Find 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 points A (a, 0, 0), B (0, b, 0) and C(0, 0, c). Reduce it to normal form. If plane ABC is at a distance p from the origin, prove that \[\frac{1}{p^2} = \frac{1}{a^2} + \frac{1}{b^2} + \frac{1}{c^2} .\]

 


Find the equation of the plane that contains the point (1, −1, 2) and is perpendicular to each of the planes 2x + 3y − 2z = 5 and x + 2y − 3z = 8.


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 line through the origin which is perpendicular to the plane  \[\vec{r} \cdot \left( \hat{i} + 2 \hat{j}  + 3 \hat{k}  \right) = 3 .\]

 

Find the equation of the plane through (2, 3, −4) and (1, −1, 3) and parallel to x-axis.

 

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


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.

 

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 equation of the plane passing through points (a, 0, 0), (0, b, 0) and (0, 0, c).

 

Write the ratio in which the plane 4x + 5y − 3z = 8 divides the line segment joining the points (−2, 1, 5) and (3, 3, 2).

 

Write the distance of the plane  \[\vec{r} \cdot \left( 2 \hat{i} - \hat{j} + 2 \hat{k} \right) = 12\] from the origin.

  

Write the equation of the plane containing the lines \[\vec{r} = \vec{a} + \lambda \vec{b} \text{ and }  \vec{r} = \vec{a} + \mu \vec{c} .\]

 

Write the intercept cut off by the plane 2x + y − z = 5 on x-axis.

 

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

 

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.

 

Find the vector equation of the plane with intercepts 3, –4 and 2 on xy and z-axis respectively.

 


Find the vector equation of the plane which contains the line of intersection of the planes `vec("r").(hat"i"+2hat"j"+3hat"k"),-4=0, vec("r").(2hat"i"+hat"j"-hat"k")+5=0`and which is perpendicular to the plane`vec("r").(5hat"i"+3hat"j"-6hat"k"),+8=0`


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`


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:


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×