If $A \equiv (x, 4, -1)$,$B \equiv (3, x, -5)$,and $C \equiv (2, -2, 3)$ are the vertices and $G \equiv (2, 1, -1)$ is the centroid of the triangle $ABC$,then the value of $x$ is
- A$3$
- B$1$
- C$-2$
- D$2$
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Similar Questions
The points $A(-1, 2, 3)$,$B(2, -3, 1)$,and $C(3, 1, -2)$:
If the circumcenter of the triangle formed by the points $(1,2,3), (3,-1,5)$ and $(4,0,-3)$ is $(\alpha, \beta, \gamma)$, then $|\alpha|+|\beta|=$
Match the following columns:
Column $I$ Column $II$ $(A)$ The centroid of the triangle formed by $(2, 3, -1)$,$(5, 6, 3)$,$(2, -3, 1)$ is $(p)$ $(2, 2, 2)$ $(B)$ The circumcentre of the triangle formed by $(1, 2, 3)$,$(2, 3, 1)$,$(3, 1, 2)$ is $(q)$ $(3, 1, 4)$ $(C)$ The orthocentre of the triangle formed by $(2, 1, 5)$,$(3, 2, 3)$,$(4, 0, 4)$ is $(r)$ $(1, 1, 0)$ $(D)$ The incentre of the triangle formed by $(0, 0, 0)$,$(3, 0, 0)$,$(0, 4, 0)$ is $(s)$ $(3, 2, 1)$
| Column $I$ | Column $II$ |
| $(A)$ The centroid of the triangle formed by $(2, 3, -1)$,$(5, 6, 3)$,$(2, -3, 1)$ is | $(p)$ $(2, 2, 2)$ |
| $(B)$ The circumcentre of the triangle formed by $(1, 2, 3)$,$(2, 3, 1)$,$(3, 1, 2)$ is | $(q)$ $(3, 1, 4)$ |
| $(C)$ The orthocentre of the triangle formed by $(2, 1, 5)$,$(3, 2, 3)$,$(4, 0, 4)$ is | $(r)$ $(1, 1, 0)$ |
| $(D)$ The incentre of the triangle formed by $(0, 0, 0)$,$(3, 0, 0)$,$(0, 4, 0)$ is | $(s)$ $(3, 2, 1)$ |
DifficultAP EAMCET 2015
View SolutionIn $\triangle ABC$,the midpoints of the sides $AB, BC$ and $CA$ are respectively $(l, 0, 0), (0, m, 0)$ and $(0, 0, n)$. Then,$\frac{AB^2+BC^2+CA^2}{l^2+m^2+n^2}$ is equal to
DifficultTS EAMCET 2008
View SolutionLet $A (2, 3, 5)$,$B (-1, 3, 2)$ and $C (\lambda, 5, \mu)$ be the vertices of a $\Delta ABC$. If the median through $A$ is equally inclined to the coordinate axes,then
DifficultJEE MAIN 2014
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