The points A(-1, 2, 3),B(2, -3, 1),and C(3, 1 | vedclass

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

Question

(D) To determine the nature of the triangle formed by points $A(-1, 2, 3)$,$B(2, -3, 1)$,and $C(3, 1, -2)$,we calculate the lengths of the sides using

Vedclass · Accepted Answer

form a scalene triangle

Vedclass · Answer

(D) To determine the nature of the triangle formed by points $A(-1, 2, 3)$,$B(2, -3, 1)$,and $C(3, 1, -2)$,we calculate the lengths of the sides using the distance formula $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}$.$1$. Length of $AB$:$AB = \sqrt{(2 - (-1))^2 + (-3 - 2)^2 + (1 - 3)^2} = \sqrt{3^2 + (-5)^2 + (-2)^2} = \sqrt{9 + 25 + 4} = \sqrt{38}$.$2$. Length of $BC$:$BC = \sqrt{(3 - 2)^2 + (1 - (-3))^2 + (-2 - 1)^2} = \sqrt{1^2 + 4^2 + (-3)^2} = \sqrt{1 + 16 + 9} = \sqrt{26}$.$3$. Length of $AC$:$AC = \sqrt{(3 - (-1))^2 + (1 - 2)^2 + (-2 - 3)^2} = \sqrt{4^2 + (-1)^2 + (-5)^2} = \sqrt{16 + 1 + 25} = \sqrt{42}$.Since all sides $AB = \sqrt{38}$,$BC = \sqrt{26}$,and $AC = \sqrt{42}$ are unequal,the triangle is a scalene triangle.

The points $A(-1, 2, 3)$,$B(2, -3, 1)$,and $C(3, 1, -2)$:

Similar Questions

If the points $A(0, 1, 2)$,$B(2, -1, 3)$,and $C(1, -3, 1)$ are the vertices of a triangle,then the triangle is

The incenter of the triangle formed by the points $(0,0,0), (3,0,0)$ and $(0,4,0)$ is

The centroid of a tetrahedron with vertices $A(3, -5, x)$,$B(5, 4, 2)$,$C(7, -7, y)$,and $D(1, 0, z)$ is $G(4, -2, 2)$. Then,the value of $x + y + z$ is:

Are the points $A(3, 6, 9)$,$B(10, 20, 30)$,and $C(25, -41, 5)$ the vertices of a right-angled triangle?

If $D(2, 1, 0)$,$E(2, 0, 0)$,and $F(0, 1, 0)$ are mid-points of the sides $BC$,$CA$,and $AB$ of $\triangle ABC$,respectively,then the centroid of $\triangle ABC$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module