Question

given the points are they parallel perpendicular skew or none of these

Answer 1

Given points are R(-1,-2), S(5,2), and T(-2,6), U(4,-3)

First find the slope of line RS and TU:

So for RS:

$\begin{gathered} m_{RS}=\frac{2-(-2)}{5-(-1)} \\ m_{RS}=\frac{2+2}{5+1}=\frac{4}{6} \\ m_{RS}=\frac{2}{3} \end{gathered}$

Now the slope of TU:

$\begin{gathered} m_{TU}=\frac{-3-6}{4-(-2)} \\ m_{TU}=-\frac{9}{6} \\ m_{TU}=-\frac{3}{2} \end{gathered}$

So the condition for both the lines are perpendicular as we know that:

For perpendicular the slope of two lines are:

$m_1=-\frac{1}{m_2}$

So option B is correct.