Question

In the Cartesian form for skew lines, what is the denominator of \[\mathbf d\]?

पर्याय

• \[\sqrt{\mathbf a_1^2+\mathbf b_1^2+\mathbf c_1^2}\]

• \[\sqrt{(\mathbf a_1\mathbf b_2-\mathbf a_2\mathbf b_1)^2+(\mathbf a_1\mathbf c_2-\mathbf a_2\mathbf c_1)^2+(\mathbf b_1\mathbf c_2-\mathbf b_2\mathbf c_1)^2}\]

• \[\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\]

• \[|\mathbf a_2-\mathbf a_1|\]

Answer 1

The denominator is the magnitude of the cross product of the two direction vectors in Cartesian components. It contains the three squared component differences formed from \[\mathbf a_i,\mathbf b_i,\mathbf c_i\].