Given triangle ABC such that A = 2hat{i} - ha | vedclass

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

Question

(B) The vertices of $	riangle ABC$ are $A(2, -1, 1)$,$B(1, -3, -5)$,and $C(3, -4, -4)$.First,we calculate the lengths of the sides using the distance

Vedclass · Accepted Answer

$A$ right-angled triangle

Vedclass · Answer

(B) The vertices of $	riangle ABC$ are $A(2, -1, 1)$,$B(1, -3, -5)$,and $C(3, -4, -4)$.First,we calculate the lengths of the sides using the distance formula:$AB = \sqrt{(1-2)^2 + (-3 - (-1))^2 + (-5-1)^2} = \sqrt{(-1)^2 + (-2)^2 + (-6)^2} = \sqrt{1 + 4 + 36} = \sqrt{41}$.$BC = \sqrt{(3-1)^2 + (-4 - (-3))^2 + (-4 - (-5))^2} = \sqrt{2^2 + (-1)^2 + 1^2} = \sqrt{4 + 1 + 1} = \sqrt{6}$.$CA = \sqrt{(2-3)^2 + (-1 - (-4))^2 + (1 - (-4))^2} = \sqrt{(-1)^2 + 3^2 + 5^2} = \sqrt{1 + 9 + 25} = \sqrt{35}$.Now,check for the Pythagorean theorem:$BC^2 + CA^2 = 6 + 35 = 41 = AB^2$.Since $AB^2 = BC^2 + CA^2$,the triangle satisfies the condition for a right-angled triangle.Thus,$	riangle ABC$ is a right-angled triangle.

Given $\triangle ABC$ such that $A = 2\hat{i} - \hat{j} + \hat{k}$,$B = \hat{i} - 3\hat{j} - 5\hat{k}$,and $C = 3\hat{i} - 4\hat{j} - 4\hat{k}$,then $\triangle ABC$ is:

Similar Questions

If the points $(-1, -1, 2), (2, m, 5)$ and $(3, 11, 6)$ are collinear,find the value of $m$.

Three vertices of a parallelogram $ABCD$ are $A(1, 2, 3)$,$B(-1, -2, -1)$ and $C(2, 3, 2)$. Find the fourth vertex $D(x, y, z)$.

Three vertices of a parallelogram are $(1, 3)$,$(2, 0)$,and $(5, 1)$. Find its fourth vertex.

The extremities of a diagonal of a parallelogram are the points $(3, -4)$ and $(-6, 5)$. If the third vertex is $(-2, 1)$,then the fourth vertex is:

The points $A(2, 3, 5)$,$B(-1, 5, -1)$,and $C(4, -3, 2)$ form:

Vedclass Test Series

Exam Paper Generator

Online Exam Module