Find the direction cosines and direction ratios of the line joining the points \mathrm{A}(1,3,5), \mathrm{B}(-1,0,-1)
Find the direction cosines and direction ratios of the line joining the points \mathrm{A}(1,3,5), \mathrm{B}(-1,0,-1)

Given the points A (1,3,5) \& B(-1,0,-1)
Direction ratios are \mathrm{a}=-1-1=-2

    \[\begin{array}{l} \mathrm{b}=0-3=-3 \\ \mathrm{c}=-1-5=-6 \end{array}\]

Now, \sqrt{a^{2}+b^{2}+c^{2}}=\sqrt{(-2)^{2}+(-3)^{2}+(-6)^{2}}=\sqrt{4+9}=36=\sqrt{49}=7
Direction cosines are

    \[\begin{array}{l} 1=\frac{a}{\sqrt{a^{2}+b^{2}+c^{2}}}=\frac{-2}{7} \\ m=\frac{b}{\sqrt{a^{2}+b^{2}+c^{2}}}=\frac{-3}{7} \\ n=\frac{c}{\sqrt{a^{2}+b^{2}+c^{2}}}=\frac{-6}{7} \end{array}\]