grandes-ecoles 2011 QIV.B.6

grandes-ecoles · France · centrale-maths2__psi Not Maths

We consider four points $U_1, U_2, U_3, U_4$ in $\mathbb{R}^3$ satisfying $U_1U_2 = U_2U_3 = U_3U_4 = U_4U_1 = 1$, $U_1U_3 = a$ and $U_2U_4 = b$. We set $\Psi(M) = -\frac{1}{2}\Phi(M)$.
Conversely, if $a^2 + b^2 \leqslant 4$, give a family of points $U_1, U_2, U_3$ and $U_4$ satisfying the mutual distance constraints.

We consider four points $U_1, U_2, U_3, U_4$ in $\mathbb{R}^3$ satisfying $U_1U_2 = U_2U_3 = U_3U_4 = U_4U_1 = 1$, $U_1U_3 = a$ and $U_2U_4 = b$. We set $\Psi(M) = -\frac{1}{2}\Phi(M)$.

Conversely, if $a^2 + b^2 \leqslant 4$, give a family of points $U_1, U_2, U_3$ and $U_4$ satisfying the mutual distance constraints.

Paper Questions

QI.A QI.B QI.C QII.A QII.B QIII.A QIII.B QIV.A.1 QIV.A.2 QIV.A.3 QIV.B.1 QIV.B.2 QIV.B.3 QIV.B.4 QIV.B.5 QIV.B.6 QV.A.1 QV.A.2 QV.B.1 QV.B.2 QV.B.3 QV.C.1 QV.C.2 QV.C.3 QV.C.4 QV.C.5 QV.C.6 QV.C.7