English

Write the Length of the Perpendicular Drawn from the Point P(3, 5, 12) on X-axis. - Mathematics

Advertisements
Advertisements

Question

Write the length of the perpendicular drawn from the point P(3, 5, 12) on x-axis.

Advertisements

Solution

The distance of the point P(3, 5, 12) from x-axis is given by 

\[\sqrt{5^2 + \left( 12 \right)^2}\]
\[ = \sqrt{169}\]
\[ = 13\]

shaalaa.com
  Is there an error in this question or solution?
Chapter 28: Introduction to three dimensional coordinate geometry - Exercise 28.4 [Page 22]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 28 Introduction to three dimensional coordinate geometry
Exercise 28.4 | Q 6 | Page 22

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

The x-axis and y-axis taken together determine a plane known as_______.


Find the image  of: 

 (–2, 3, 4) in the yz-plane.


A cube of side 5 has one vertex at the point (1, 0, –1), and the three edges from this vertex are, respectively, parallel to the negative x and y axes and positive z-axis. Find the coordinates of the other vertices of the cube.


Planes are drawn parallel to the coordinate planes through the points (3, 0, –1) and (–2, 5, 4). Find the lengths of the edges of the parallelepiped so formed.


The coordinates of a point are (3, –2, 5). Write down the coordinates of seven points such that the absolute values of their coordinates are the same as those of the coordinates of the given point.


Determine the points in zx-plane are equidistant from the points A(1, –1, 0), B(2, 1, 2) and C(3, 2, –1). 


Find the point on y-axis which is equidistant from the points (3, 1, 2) and (5, 5, 2).


Prove that the point A(1, 3, 0), B(–5, 5, 2), C(–9, –1, 2) and D(–3, –3, 0) taken in order are the vertices of a parallelogram. Also, show that ABCD is not a rectangle.


If A(–2, 2, 3) and B(13, –3, 13) are two points.
Find the locus of a point P which moves in such a way the 3PA = 2PB.


Find the locus of P if PA2 + PB2 = 2k2, where A and B are the points (3, 4, 5) and (–1, 3, –7).


Show that the points (a, b, c), (b, c, a) and (c, a, b) are the vertices of an equilateral triangle. 


Verify the following: 

 (0, 7, –10), (1, 6, –6) and (4, 9, –6) are vertices of an isosceles triangle. 


Verify the following:

 (5, –1, 1), (7, –4,7), (1, –6,10) and (–1, – 3,4) are the vertices of a rhombus.


Find the equation of the set of the points P such that its distances from the points A(3, 4, –5) and B(–2, 1, 4) are equal.


Write the distance of the point P (2, 3,5) from the xy-plane.


Write the coordinates of the foot of the perpendicular from the point (1, 2, 3) on y-axis.


Find the ratio in which the line segment joining the points (2, 4,5) and (3, −5, 4) is divided by the yz-plane.


Find the point on y-axis which is at a distance of  \[\sqrt{10}\] units from the point (1, 2, 3).


The coordinates of the foot of the perpendicular from a point P(6,7, 8) on x - axis are 


Find the direction cosines of the line passing through the points P(2, 3, 5) and Q(–1, 2, 4).


A plane meets the co-ordinates axis in A, B, C such that the centroid of the ∆ABC is the point (α, β, γ). Show that the equation of the plane is `x/alpha + y/beta + z/γ` = 3


Find the co-ordinates of the foot of perpendicular drawn from the point A(1, 8, 4) to the line joining the points B(0, –1, 3) and C(2, –3, –1).


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


If a line makes an angle of `pi/4` with each of y and z axis, then the angle which it makes with x-axis is ______.


If the line drawn from the point (–2, – 1, – 3) meets a plane at right angle at the point (1, – 3, 3), find the equation of the plane


Find the equations of the two lines through the origin which intersect the line `(x - 3)/2 = (y - 3)/1 = z/1` at angles of `pi/3` each.


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)`


Show that the points `(hati - hatj + 3hatk)` and `3(hati + hatj + hatk)` are equidistant from the plane `vecr * (5hati + 2hatj - 7hatk) + 9` = 0 and lies on opposite side of it.


If l1, m1, n1 ; l2, m2, n2 ; l3, m3, n3 are the direction cosines of three mutually perpendicular lines, prove that the line whose direction cosines are proportional to l1 + l2 + l3, m1 + m2 + m3, n1 + n2 + n3 makes equal angles with them.


If the directions cosines of a line are k, k, k, then ______.


The area of the quadrilateral ABCD, where A(0, 4, 1), B(2,  3, –1), C(4, 5, 0) and D(2, 6, 2), is equal to ______.


The unit vector normal to the plane x + 2y +3z – 6 = 0 is `1/sqrt(14)hati + 2/sqrt(14)hatj + 3/sqrt(14)hatk`.


The intercepts made by the plane 2x – 3y + 5z +4 = 0 on the co-ordinate axis are `-2, 4/3, - 4/5`.


The line `vecr = 2hati - 3hatj - hatk + lambda(hati - hatj + 2hatk)` lies in the plane `vecr.(3hati + hatj - hatk) + 2` = 0.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×