Medium Practice — Set 1

Quick Recap — Lines in Space

• Vector form: $\vec r=\vec a+\lambda\vec b$; Cartesian: $\tfrac{x-x_1}{a}=\tfrac{y-y_1}{b}=\tfrac{z-z_1}{c}$.
• Angle between lines: $\cos\theta=\dfrac{|a_1a_2+b_1b_2+c_1c_2|}{\sqrt{\sum a_1^2}\sqrt{\sum a_2^2}}$.
• Parallel iff dr's proportional; perpendicular iff $a_1a_2+b_1b_2+c_1c_2=0$.
• Skew lines are neither parallel nor intersecting; intersecting lines are coplanar.