Question

Find the direction cosines of the line joining $A(0,7,10)$ and $B(-1,6,6)$.

• A. $\frac{-1}{3\sqrt{2}}$, $\frac{-1}{3\sqrt{2}}$, $\frac{2}{3\sqrt{2}}$
• B. $\frac{1}{3\sqrt{2}}$, $\frac{1}{3\sqrt{2}}$, $\frac{4}{3\sqrt{2}}$
• C. $\frac{1}{3}$, $\frac{-1}{3}$, $\frac{4}{3}$
• D. None of these

Answer 1

Answer: (B)

Direction ratios of $AB$ are $\left(-1,-0,6-7,6-10\right)$
or $\left(-1,-1,-4\right)$
Also, $\sqrt{{\left(-1\right)}^2+{\left(-1\right)}^2+{\left(-4\right)}^2}$
$=3\sqrt{2}$
$\therefore$ Direction cosines are $\left(-\frac{1}{3\sqrt{2}},-\frac{1}{3\sqrt{2}},\frac{-4}{3\sqrt{2}}\right)$
or $\left(\frac{1}{3\sqrt{2}},\frac{1}{3\sqrt{2}},\frac{4}{3\sqrt{2}}\right)$