Mathematics

Mathematics

Problem

The position vector of the point of intersection of three planes r⋅n1=q1,r⋅n2=q2,r⋅n3=q3\mathbf{r} \cdot \mathbf{n}_1 = q_1, \mathbf{r} \cdot \mathbf{n}_2 = q_2, \mathbf{r} \cdot \mathbf{n}_3 = q_3 , where n1,n2\mathbf{n}_1, \mathbf{n}_2 and n3\mathbf{n}_3 are non-coplanar vectors, is a. 1[n1n2n3][q3(n1×n2)+q1(n2×n3)+q2(n3×n1)]\frac{1}{[\mathbf{n}_1 \mathbf{n}_2 \mathbf{n}_3]} [q_3 (\mathbf{n}_1 \times \mathbf{n}_2) + q_1 (\mathbf{n}_2 \times \mathbf{n}_3) + q_2 (\mathbf{n}_3 \times \mathbf{n}_1)] b. 1[n1n2n3][q1(n1×n2)+q2(n2×n3)+q3(n3×n1)]\frac{1}{[\mathbf{n}_1 \mathbf{n}_2 \mathbf{n}_3]} [q_1 (\mathbf{n}_1 \times \mathbf{n}_2) + q_2 (\mathbf{n}_2 \times \mathbf{n}_3) + q_3 (\mathbf{n}_3 \times \mathbf{n}_1)] c. −1[n3n1n2][q1(n1×n2)+q2(n2×n3)+q3(n3×n1)]-\frac{1}{[\mathbf{n}_3 \mathbf{n}_1 \mathbf{n}_2]} [q_1 (\mathbf{n}_1 \times \mathbf{n}_2) + q_2 (\mathbf{n}_2 \times \mathbf{n}_3) + q_3 (\mathbf{n}_3 \times \mathbf{n}_1)] d. None of the above

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