Easy Practice — Set 2

Quick Recap — Direction Ratios & Planes

• If direction ratios are $(a,b,c)$, direction cosines are $\Big(\tfrac{a}{\sqrt{a^2+b^2+c^2}},\dots\Big)$.
• General plane: $ax+by+cz+d=0$, with normal $(a,b,c)$; through the origin iff $d=0$.
• Distance of a point $(x_1,y_1,z_1)$ from the plane: $\dfrac{|ax_1+by_1+cz_1+d|}{\sqrt{a^2+b^2+c^2}}$.
• Intercept form: $\tfrac xa+\tfrac yb+\tfrac zc=1$; normal form: $lx+my+nz=p$.