Tetrahedron

Q. If
a = Number of vertices of a tetrahedron
b = Number of edges of a tetrahedron
c = Number of faces of a tetrahedron
then the value of a + b + c =

1. 10
2. 14
3. 15
4. 20

Q. The position vectors of the vertices $A,B$ and $C$ of a tetrahedron are $(1,1,1),$ $(1,0,0)$ and $(3,0,0)$ respectively. The altitude from the vertex $D$ to the opposite face $ABC$ meets the median line through $A$ of the $\Delta ABC$ at a point $E.$ If the length of side $AD$ is $4$ units and volume of the tetrahedron is $\frac{2\sqrt{2}}{3}$ cubic units, then the CORRECT statement(s) is (are)

1. The length of altitude from the vertex $D$ is $2$.
2. There is exactly one position for the point $E$.
3. There can be two positions for the point $E$.
4. Vector $\hat{j}-\hat{k}$ is normal to the plane $ABC$.

Q. Given that P(3, 2, –4), Q(5, 4, –6) and R(9, 8, –10) are collinear. Find the ratio in which Q divides PR.

Q.

let ABC be triangle having orthocenter circumcenter at (9, 5) (0, 0) respectively if equation of side BC is2x-y=10 then find possible coordinte of vertex A.

Q. a = Number of vertices of a tetrahedron
b = Number of edges of a tetrahedron
c = Number of faces of a tetrahedron
Find the value of a+b+c

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