CameraIcon

SearchIcon

MyQuestionIcon

4

You visited us 4 times! Enjoying our articles? Unlock Full Access!

Distance Formula

Find the coor...

Question

Find the coordinates of the point which is equidistant from the points A(a, 0, 0), B(0, b, 0), C(0, 0, c) and O(0, 0, 0).

Open in App

Solution

Let the required point be P(x, y, z). Then,

$P A^{2} = P B^{2} = P C^{2} = P O^{2} \Leftrightarrow P A^{2} - P O^{2} = 0, P B^{2} - P O^{2} = 0$ and $P C^{2} - P O^{2} = 0$ .

Suggest Corrections

thumbs-up

1

Similar questions

Q. The coordinates of the point equidistant from the four points O(0, 0, 0), A(a, 0, 0), B(0, b, 0) and C(0, 0, c) are ________________________.

Q. The point equidistant from the point

O (0, 0, 0), A (a, 0, 0), B (0, b, 0)

C (0, 0, c)

has the coordinates

Q. Find the orthocentre of the triangle whose vertices are

A (a, 0, 0), B (0, b, 0), C (0, 0, c)

Q. 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}} .

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Distance Formula

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Distance Formula

Standard XI Mathematics

Join BYJU'S Learning Program

CrossIcon