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

Question

The perimeter of the triangle with vertices at (1,0,0),(0,1,0) and (0,0,1) is (A) 3 (B) 2 (C) 2 √2 (D) 3 √2

Tardigrade Admin · Accepted Answer

Let A=(1,0,0), B=(0,1,0) and C=(0,0,1) Now, A B=√(0-1)2+(1-0)2+02=√2 B C=√02+(0-1)2+(1-0)2=√2 and C A=√(1-0)2+02+(0-1)2=√2 ∴ Perimeter of triangle =A B+B C+C A =√2+√2+√2=3 √2

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

3

2

$22$

$32$

Let $A = (1, 0, 0), B = (0, 1, 0)$ and $C = (0, 0, 1)$
Now, $A B = (0 - 1)^{2} + (1 - 0)^{2} + 0^{2} = 2$
$BC = 0^{2} + (0 - 1)^{2} + (1 - 0)^{2} = 2$
and $C A = (1 - 0)^{2} + 0^{2} + (0 - 1)^{2} = 2$
$∴$ Perimeter of triangle $= A B + BC + C A$
$= 2 + 2 + 2 = 32$

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

3

2

22​

32​

Let A=(1,0,0),B=(0,1,0) and C=(0,0,1) Now, AB=(0−1)2+(1−0)2+02​=2​ BC=02+(0−1)2+(1−0)2​=2​ and CA=(1−0)2+02+(0−1)2​=2​ ∴ Perimeter of triangle =AB+BC+CA =2​+2​+2​=32​

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

$22$

$32$

Let $A = (1, 0, 0), B = (0, 1, 0)$ and $C = (0, 0, 1)$
Now, $A B = (0 - 1)^{2} + (1 - 0)^{2} + 0^{2} = 2$
$BC = 0^{2} + (0 - 1)^{2} + (1 - 0)^{2} = 2$
and $C A = (1 - 0)^{2} + 0^{2} + (0 - 1)^{2} = 2$
$∴$ Perimeter of triangle $= A B + BC + C A$
$= 2 + 2 + 2 = 32$