Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Three Dimensional Geometry
0 votes

The direction cosines of the vector $(2\hat i+2\hat j-\hat k)$ are ___________.

$\begin{array}{1 1} (A)\;\bigg(\large\frac{2}{3},\frac{-2}{3},\frac{-1}{3}\bigg) \\ (B)\;\bigg(\large\frac{2}{3},\frac{2}{3},\frac{1}{3}\bigg) \\(C)\;\bigg(\large\frac{2}{3},\frac{2}{3},\frac{-1}{3}\bigg) \\(D)\;\bigg(\large\frac{2}{5},\frac{2}{5},\frac{-1}{5}\bigg) \end{array} $

Can you answer this question?

1 Answer

0 votes
  • If a directed line segement $OP$ makes angles $\alpha,\beta,\gamma$ with $OX,OY$ and $OZ$ respectively, then $\cos \alpha, \cos \beta, \cos \gamma$ are known as the direction cosines of $OP$
The direction cosines of the vector $(2 \hat i+2 \hat j-\hat k)$ can be determined as follows
Let $\overrightarrow a=2 \hat i+2 \hat j-\hat k$
The magnitude of $\overrightarrow a$ is $|\overrightarrow a|=\sqrt {2^2+2^2+(-1)^2}$
$|\overrightarrow a|=\sqrt 9=3$
Therefore direction cosines is $\bigg(\large\frac{2}{3},\frac{2}{3},\frac{-1}{3}\bigg)$
answered Jun 12, 2013 by meena.p

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App