Question

A vector $\overrightarrow{r}$ has length $21$ and direction ratio's $2,-3,6$ the direction cosines of $\overrightarrow{r}$,given that $\overrightarrow{r}$ makes an obtuse angle with x-axis is given by

• A. $\frac{2}{7},\frac{-3}{7},\frac{6}{7}$
• B. $\frac{-2}{7},\frac{3}{7},\frac{6}{7}$
• C. $\frac{-2}{7},\frac{3}{7},\frac{-6}{7}$
• D. $1,0,0$

Answer 1

The correct option is A $\frac{2}{7},\frac{-3}{7},\frac{6}{7}$

We have,

$l,m,n$ are direrction cosines.

$l^2+m^2+n^2=1\left(a,-b,c\right)=\left(2,-3,6\right)$

$\left(4,9,36\right){\alpha }^2=1l=\lambda am=\lambda bn=\lambda c$

$\lambda =\pm \frac{1}{7}$

But,

$\lambda =-\frac{1}{7}$ because $\overrightarrow{r}$ makes are obtuse angle with $X-axis$.

Therefore cosines are $\frac{-2}{7},\frac{3}{7},\frac{-6}{7}$

Hence,

Option $C$ is correct answer.