The coordinates of the point R which divides the line segment joining two points P x 1- y 1- z 1 and Q x 2- y 2- z 2 externally in the ratio m - n are given byA- m x2-n x1-m-n- m y2-n y1-m-n- m z2-n z1-m-nB- m x2-n x1-m-n- m y2-n y1-m-n- m z2-n z1-m-nm x2-n x1-m-n- m y2-n y1-m-n- m z2-n z1-m-nD- m x2-n x1-m-n- m y2-n y1-m-n- m z2-n z1-m-n

The correct option is D nbsp; nbsp; nbsp; nbsp; ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

External Division

The coordinat...

Question

The coordinates of the point R which divides the line segment joining two points P (x₁, y₁, z₁) and Q (x₂, y₂, z₂) externally in the ratio m : n are given by

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D

Suggest Corrections

Similar questions

Let $P (x_{1}, y_{1}, z_{1})$ and $Q (x_{2}, y_{2}, z_{2})$ be two points and let R(x, y, z) be a point on PQ dividing it in the ratio m:n. Prove that
$x = \frac{m x_{2} + n x_{1}}{m + n}, y = \frac{m y_{2} + n y_{1}}{m + n}$ and $z = \frac{m z_{2} + n z_{1}}{m + n}$ .

Which of the follwing statements are correct ?
1. The coordinates of the point R which divides the line

segment joining two points $P (x_{1}, y_{1}, z_{1})$ and $Q (x_{2}, y_{2}, z_{2})$

externally in the ratio m:n are $(\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n}, \frac{m z_{2} + n z_{1}}{m + n})$ .

2. If R divides PQ internally in the ratio m:n, then its coordinates

are obtained by replacing n by -n in the statement 1.

Q. If P(x,y) divides A

(x_{1}, y_{1})

and B

(x_{2}, y_{2})

in the ratio m : n, then, P(x,y) =

(\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n})

Q. Assertion :STATEMENT- 1 : A straight line passing through the origin intersects the branches of the hyperbola xy = 9 at Q in the first and R in the third quadrant. The point P divides the segment QR internally in the ratio 1:2, then the locus of P is ellipse Reason: STATEMENT- 2 :

A \equiv (x_{1}, y_{1}), B \equiv (x_{2}, y_{2})

If P divides line joining Aand B in the ratio m : n, then co-ordinates of P are

[\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n}]

Q. If

l (m - n) x^{2} + m (n - l) x y + n (l - m) y^{2}

is a perfect square, then the quantities

l, m, n

are in

Join BYJU'S Learning Program

The coordinates of the point R which divides the line segment joining two points P (x1, y1, z1) and Q (x2, y2, z2) externally in the ratio m : n are given by

The correct option is D

The coordinates of the point R which divides the line segment joining two points P (x₁, y₁, z₁) and Q (x₂, y₂, z₂) externally in the ratio m : n are given by