Mathematics

Problem

Match the statement of Column I with values of Column II.

Column I	Column II
A. Let $O$ be an interior point of $\triangle ABC$ such that $OA + 2OB + 3OC = 0$ , then the ratio of the area of $\triangle ABC$ to the area of $\triangle AOC$ , with $O$ as the origin	p. 0
B. $A \cdot B = A \cdot C = 0$ , $B \cdot C = 3/2$ <br> $A \cdot A = B \cdot B = C \cdot C = 1$ , $[\mathbf{A} \mathbf{B} \mathbf{C}] =$	q. $\frac{1}{2}$
C. If $\mathbf{a}$ , $\mathbf{b}$ , $\mathbf{c}$ and $\mathbf{d}$ are non-zero vectors such that no three of them are in the same plane and no two are orthogonal, then the value of the scalar $\frac{(\mathbf{b} \times \mathbf{c}) \cdot (\mathbf{a} \times \mathbf{d}) + (\mathbf{c} \times \mathbf{a}) \cdot (\mathbf{b} \times \mathbf{d})}{(\mathbf{a} \times \mathbf{b}) \cdot (\mathbf{d} \times \mathbf{c})}$ is	r. 2