The perimeter of the triangle with vertices a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the vertices of the triangle be $A = (1, 0, 0)$,$B = (0, 1, 0)$,and $C = (0, 0, 1)$.Using the distance formula $d = \sqrt{(x_2-x_1)^2 + (y_2-y

Vedclass · Accepted Answer

$3 \sqrt{2}$

Vedclass · Answer

(D) Let the vertices of the triangle be $A = (1, 0, 0)$,$B = (0, 1, 0)$,and $C = (0, 0, 1)$.Using the distance formula $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}$,we calculate the lengths of the sides:$AB = \sqrt{(0-1)^2 + (1-0)^2 + (0-0)^2} = \sqrt{(-1)^2 + 1^2 + 0^2} = \sqrt{1+1} = \sqrt{2}$.$BC = \sqrt{(0-0)^2 + (0-1)^2 + (1-0)^2} = \sqrt{0^2 + (-1)^2 + 1^2} = \sqrt{1+1} = \sqrt{2}$.$CA = \sqrt{(1-0)^2 + (0-0)^2 + (0-1)^2} = \sqrt{1^2 + 0^2 + (-1)^2} = \sqrt{1+1} = \sqrt{2}$.The perimeter of the triangle is the sum of the lengths of its sides:$	ext{Perimeter} = AB + BC + CA = \sqrt{2} + \sqrt{2} + \sqrt{2} = 3\sqrt{2}$.

The perimeter of the triangle with vertices at $(1,0,0), (0,1,0)$ and $(0,0,1)$ is

Similar Questions

According to the Bentham and Hooker system of classification,which of the following are the main divisions of the plant kingdom?

Two particles $P$ and $Q$ start from the origin and execute Simple Harmonic Motion along the $X$-axis with the same amplitude but with periods $3 \ s$ and $6 \ s$ respectively. The ratio of the velocities of $P$ and $Q$ when they meet is

Which one of the following reactions represents the oxidising property of $H_2O_2$?

Which of the following is a conjugate acid-base pair?

$A$ man standing on a road has to hold his umbrella at $30^{\circ}$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10 ~km/h$. He finds that raindrops are hitting his head vertically. The actual speed of raindrops is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module