CameraIcon

SearchIcon

MyQuestionIcon

1

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

Centroid Formula

Using vector ...

Question

Using vector method, find the incentre of triangle whose vertices are $P (0, 4, 0), Q (0, 0, 3), R (0, 4, 3)$ .

Open in App

Solution

Let $\to p, \to q, \to r$ be the position vector of vertices P,Q,R of $Δ P Q R$ respectively.
$\begin{matrix} \to p = 4 ˆ j, \to q = 3 ˆ k, \to r = 4 \to j + 3 ˆ k - - \to P Q = \to q - \to p = 3 ˆ k - 4 ˆ j = - 4 ˆ j + 3 ˆ k - - \to Q R = \to r - \to q = 4 \to j + 3 ˆ k - 3 ˆ k = 4 \to j - - \to R P = \to p - \to r = 4 ˆ j - 4 \to j - 3 ˆ k = - 3 ˆ k L e t x, y, z b e t h e l e n g t h o f o p p o s i t e o f v e r t i c e s P, Q, R r e s p e c t i v e l y x = ∣ ∣ ∣ - - \to Q R ∣ ∣ ∣ = 4 y = ∣ ∣ ∣ - - \to R P ∣ ∣ ∣ = 3 z = ∣ ∣ ∣ - - \to P Q ∣ ∣ ∣ = \sqrt{16 + 9} = \sqrt{25} = 5 \end{matrix}$
If H( $\to h$ ) is the incentre of $Δ P Q R$ then
$\begin{matrix} \to h = \frac{x \to p + y \to q + z \to r}{x + y + z} \frac{4 (4 ˆ j) + 3 (3 ˆ k) + 5 (4 ˆ j + 3 ˆ k)}{4 + 3 + 5} \frac{16 ˆ j + 9 ˆ k + 20 ˆ j + 15 ˆ k}{12} \frac{36 ˆ j + 24 ˆ k}{12} = 3 ˆ j + 3 ˆ k \end{matrix}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Using vector method, find the incentre of the triangle whose vertices are

P (0, 4, 0), Q (0, 0, 3)

R (0, 4, 3)

Q. Using vector method, find the area of the triangle whose vertices

(1, 1, 2), (2, 3, 5)

(1, 5, 5)

Q. Find the incentre of the triangle whose vertices are

(2, 3), (- 2, - 5), (- 4, 6)

Q. Find the coordinates of incentre of the triangle whose vertices are

(7, - 36), (7, 20)

(- 8, 0)

Q. Find the co-ordinates of the incentre of the triangle whose vertices are

(- 2, 4), (5, 5)

(4, - 2)

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Centroid Formula

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Centroid Formula

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon