English

Find the distance between the pairs of points: (2, 3, 5) and (4, 3, 1) - Mathematics

Advertisements
Advertisements

Question

Find the distance between the pairs of points:

(2, 3, 5) and (4, 3, 1)

Sum

Solution

The distance between points P(x1, y1, z1) and P(x2, y2, z2) is given by 

= `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2)`

Distance between points (2, 3, 5) and (4, 3, 1)

= `sqrt((4 - 2)^2 + (3 - 3)^2 + (1 - 5)^2)`

= `sqrt(2^2 + 0^2 + (4)^2)`

= `sqrt(4 + 16)`

= `sqrt20`

= `2sqrt5`

shaalaa.com
  Is there an error in this question or solution?
Chapter 12: Introduction to Three Dimensional Geometry - Exercise 12.2 [Page 273]

APPEARS IN

NCERT Mathematics [English] Class 11
Chapter 12 Introduction to Three Dimensional Geometry
Exercise 12.2 | Q 1.1 | Page 273

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Find the distance between the following pairs of points:

(–3, 7, 2) and (2, 4, –1)


Find the distance between the following pairs of points:

(–1, 3, –4) and (1, –3, 4)


Show that the points (–2, 3, 5), (1, 2, 3) and (7, 0, –1) are collinear.


Verify the following:

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


Verify the following:

(0, 7, 10), (–1, 6, 6) and (–4, 9, 6) are the vertices of a right angled triangle.


Find the equation of the set of points P, the sum of whose distances from A (4, 0, 0) and B (–4, 0, 0) is equal to 10.


Find the distance between the following pairs of points: 

P(1, –1, 0) and Q(2, 1, 2)


Find the distance between the following pairs of point: 

A(3, 2, –1) and B(–1, –1, –1).


Find the distance between the points P and Q having coordinates (–2, 3, 1) and (2, 1, 2).


Using distance formula prove that the following points are collinear:

A(4, –3, –1), B(5, –7, 6) and C(3, 1, –8)


Using distance formula prove that the following points are collinear: 

P(0, 7, –7), Q(1, 4, –5) and R(–1, 10, –9)


Using distance formula prove that the following points are collinear: 

A(3, –5, 1), B(–1, 0, 8) and C(7, –10, –6)


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


Show that the points (0, 7, 10), (–1, 6, 6) and (–4, 9, 6) are the vertices of an isosceles right-angled triangle. 


Show that the points A(1, 3, 4), B(–1, 6, 10), C(–7, 4, 7) and D(–5, 1, 1) are the vertices of a rhombus. 


Show that the points (3, 2, 2), (–1, 4, 2), (0, 5, 6), (2, 1, 2) lie on a sphere whose centre is (1, 3, 4). Find also its radius.


Find the distance of the point (– 2, 4, – 5) from the line `(x + 3)/3 = (y - 4)/5 = (z + 8)/6`


Find the distance of the point (–1, –5, – 10) from the point of intersection of the line `vecr = 2hati - hatj + 2hatk + lambda(3hati + 4hatj + 2hatk)` and the plane `vecr * (hati - hatj + hatk)` = 5.


The distance of a point P(a, b, c) from x-axis is ______.


Find the angle between the lines `vecr = 3hati - 2hatj + 6hatk + lambda(2hati + hatj + 2hatk)` and `vecr = (2hatj - 5hatk) + mu(6hati + 3hatj + 2hatk)`


Find the equation of a plane which is at a distance `3sqrt(3)` units from origin and the normal to which is equally inclined to coordinate axis


Find the distance of a point (2, 4, –1) from the line `(x + 5)/1 = (y + 3)/4 = (z - 6)/(-9)`


Find the shortest distance between the lines given by `vecr = (8 + 3lambdahati - (9 + 16lambda)hatj + (10 + 7lambda)hatk` and `vecr = 15hati + 29hatj + 5hatk + mu(3hati + 8hatj - 5hatk)`


Find the equation of the plane through the intersection of the planes `vecr * (hati + 3hatj) - 6` = 0 and `vecr * (3hati + hatj + 4hatk)` = 0, whose perpendicular distance from origin is unity.


Distance of the point (α, β, γ) from y-axis is ______.


If one of the diameters of the circle x2 + y2 – 2x – 6y + 6 = 0 is a chord of another circle 'C' whose center is at (2, 1), then its radius is ______.


The points A(5, –1, 1); B(7, –4, 7); C(1, –6, 10) and D(–1, –3, 4) are vertices of a ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×