logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  CBSE XII  >>  Math  >>  Model Papers
0 votes

Find the angle between the vectors : $ \overrightarrow a = \hat i - \hat j + \hat k\: and \: \overrightarrow b = \hat i + \hat j -\hat k$

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • The scalar product of two vectors is $\overrightarrow a.\overrightarrow b=\mid \overrightarrow a\mid\mid\overrightarrow b\mid\cos\theta$
  • Hence the angle between two vectors is given by $\cos\theta=\large\frac{\overrightarrow a.\overrightarrow b}{\mid\overrightarrow a\mid\mid\overrightarrow b\mid}$
Step 1:
$\overrightarrow a=\hat i-\hat j+\hat k$
$\overrightarrow b=\hat i+\hat j-\hat k$
$\cos\theta=\large\frac{\overrightarrow a.\overrightarrow b}{\mid\overrightarrow a\mid\mid\overrightarrow b\mid}$
$\overrightarrow a.\overrightarrow b=(\hat i-\hat j+\hat k).(\hat i+\hat j-\hat k)$
$\qquad\;=1-1-1$
$\qquad\;=-1$
Step 2:
$\mid\overrightarrow a \mid=\sqrt{1^2+(-1)^2+(1)^2}$
$\mid\overrightarrow a \mid=\sqrt 3$
$\mid\overrightarrow b \mid=\sqrt{1^2+(1)^2+(-1)^2}$
$\mid\overrightarrow b \mid=\sqrt 3$
$\cos\theta=\large\frac{\overrightarrow a.\overrightarrow b}{\mid\overrightarrow a\mid\mid\overrightarrow b\mid}$
$\qquad=\large\frac{-1}{3}$
$\theta=\cos^{-1}\big(\large\frac{-1}{3}\big)$
answered Sep 26, 2013 by sreemathi.v
 

Related questions

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