grandes-ecoles 2011 QIV.B.4

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 $\Psi(M) = -\frac{1}{2}\Phi(M)$.
What equality do the reals $a$ and $b$ satisfy when the points $U_1, U_2, U_3$ and $U_4$ are coplanar?

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 $\Psi(M) = -\frac{1}{2}\Phi(M)$.

What equality do the reals $a$ and $b$ satisfy when the points $U_1, U_2, U_3$ and $U_4$ are coplanar?

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