Consider the tetrahedron with the vertices A( | vedclass

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

Question

(C) The vertices of the tetrahedron are $A(3,2,4)$,$B(x_1, y_1, 0)$,$C(x_2, y_2, 0)$,and $D(x_3, y_3, 0)$.Triangle $BCD$ is formed by the intersection

Vedclass · Accepted Answer

$\left(3, \frac{7}{4}, 1\right)$

Vedclass · Answer

(C) The vertices of the tetrahedron are $A(3,2,4)$,$B(x_1, y_1, 0)$,$C(x_2, y_2, 0)$,and $D(x_3, y_3, 0)$.Triangle $BCD$ is formed by the intersection of lines $y=x$,$x+y=6$,and $y=1$.Solving for the intersection points:$1$) $y=x$ and $y=1 \Rightarrow x=1$. Vertex $B = (1,1,0)$.$2$) $x+y=6$ and $y=1 \Rightarrow x=5$. Vertex $D = (5,1,0)$.$3$) $y=x$ and $x+y=6 \Rightarrow 2x=6 \Rightarrow x=3, y=3$. Vertex $C = (3,3,0)$.The centroid $G$ of a tetrahedron with vertices $(x_1, y_1, z_1), (x_2, y_2, z_2), (x_3, y_3, z_3), (x_4, y_4, z_4)$ is given by $\left(\frac{\sum x_i}{4}, \frac{\sum y_i}{4}, \frac{\sum z_i}{4}\right)$.$G = \left(\frac{3+1+3+5}{4}, \frac{2+1+3+1}{4}, \frac{4+0+0+0}{4}\right) = \left(\frac{12}{4}, \frac{7}{4}, \frac{4}{4}\right) = \left(3, \frac{7}{4}, 1\right)$.

Consider the tetrahedron with the vertices $A(3,2,4)$,$B(x_1, y_1, 0)$,$C(x_2, y_2, 0)$,and $D(x_3, y_3, 0)$. If the triangle $BCD$ is formed by the lines $y=x$,$x+y=6$,and $y=1$,then the centroid of the tetrahedron is

Similar Questions

If $A(0,1,2)$,$B(2,-1,3)$,and $C(1,-3,1)$ are the vertices of a triangle,then the distance between its circumcentre and orthocentre is

$A$ square $ABCD$ of diagonal $2a$ is folded along the diagonal $AC$ so that the planes $DAC$ and $BAC$ are at a right angle. The shortest distance between $DC$ and $AB$ is

$A$ tetrahedron of volume $5$ has three of its vertices at the points $A(2,1,-1)$,$B(3,0,1)$,and $C(2,-1,3)$. If the fourth vertex $D$ lies on the $y$-axis,then the sum of the ordinates of all possible points $D$ is-

Find the distance of the point $P(-\hat{i} + 2\hat{j} + 6\hat{k})$ from the line passing through the point $A(2, 3, -4)$ and parallel to the vector $\vec{v} = 6\hat{i} + 3\hat{j} - 4\hat{k}$.

Find the length of the perpendicular drawn from the point $P(2\hat{i} - \hat{j} + 5\hat{k})$ to the line $\vec{r} = (11\hat{i} - 2\hat{j} - 8\hat{k}) + \lambda(10\hat{i} - 4\hat{j} - 11\hat{k})$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module