Question

For parallel lines with common direction vector \[\vec{b}\], which expression gives \[SD\]?

Options

• \[SD=\left|\frac{\vec{b}_1\times\vec{b}_2}{|\vec{a}_2-\vec{a}_1|}\right|\]

• \[SD=\left|\frac{(\vec{a}_2-\vec{a}_1)\cdot(\vec{b}_1\times\vec{b}_2)}{|\vec{b}_1\times\vec{b}_2|}\right|\]

• \[SD=\left|\frac{(\vec{a}_2-\vec{a}_1)\times\vec{b}}{|\vec{b}|}\right|\]

• \[ SD = |\vec{a}_{2} - \vec{a}_{1}| + |\vec{b}| \]

Answer 1

For parallel lines, the direction vector is \[\vec{b}\]. The magnitude of \[(\vec{a}_2-\vec{a}_1)\times\vec{b}\], divided by \[|\vec{b}|\], gives the shortest distance.