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MATHEMATICS · Single correct · ISC · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry
Problem The position vector of the point of intersection of three planes r ⋅ n 1 = q 1 , r ⋅ n 2 = q 2 , r ⋅ n 3 = q 3 \mathbf{r} \cdot \mathbf{n}_1 = q_1, \mathbf{r} \cdot \mathbf{n}_2 = q_2, \mathbf{r} \cdot \mathbf{n}_3 = q_3 r ⋅ n 1 = q 1 , r ⋅ n 2 = q 2 , r ⋅ n 3 = q 3 n 1 , n 2 \mathbf{n}_1, \mathbf{n}_2 n 1 , n 2 n 3 \mathbf{n}_3 n 3 1 [ n 1 n 2 n 3 ] [ q 3 ( n 1 × n 2 ) + q 1 ( n 2 × n 3 ) + q 2 ( n 3 × n 1 ) ] \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)] [ n 1 n 2 n 3 ] 1 [ q 3 ( n 1 × n 2 ) + q 1 ( n 2 × n 3 ) + q 2 ( n 3 × n 1 )] 1 [ n 1 n 2 n 3 ] [ q 1 ( n 1 × n 2 ) + q 2 ( n 2 × n 3 ) + q 3 ( n 3 × n 1 ) ] \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)] [ n 1 n 2 n 3 ] 1 [ q 1 ( n 1 × n 2 ) + q 2 ( n 2 × n 3 ) + q 3 ( n 3 × n 1 )] − 1 [ n 3 n 1 n 2 ] [ q 1 ( n 1 × n 2 ) + q 2 ( n 2 × n 3 ) + q 3 ( n 3 × n 1 ) ] -\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)] − [ n 3 n 1 n 2 ] 1 [ q 1 ( n 1 × n 2 ) + q 2 ( n 2 × n 3 ) + q 3 ( n 3 × n 1 )] Browse the problem library