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 a vector of magnitude 5 units, and parallel to the resultant of the vectors \( \overrightarrow a = 2\hat i + 3\hat j - \hat k \: and \: \overrightarrow b = \hat i - 2\hat j + \hat k\)

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • Vector which is parallel with magnitude is $\pm \large\frac{\overrightarrow a+\overrightarrow b}{\mid \overrightarrow a+\overrightarrow b\mid}$
Step 1:
$\overrightarrow a=2\hat i+3\hat j-\hat k$
$\overrightarrow b= i-2\hat j+\hat k$
The resultant vector is $\overrightarrow a+\overrightarrow b=(2\hat i+3\hat j-\hat k+\hat i-2\hat j+\hat k)$
$\Rightarrow 3\hat i+\hat j$
Step 2:
Vector which is parallel to the above with magnitude 5 is $\pm \large\frac{\overrightarrow a+\overrightarrow b}{\mid \overrightarrow a+\overrightarrow b\mid}$
$\Rightarrow \pm\large\frac{(3\hat i+\hat j}{\sqrt{3^2+1^2}}$
$\Rightarrow \pm\large\frac{(3\hat i+\hat j}{\sqrt{10}}$
$\Rightarrow \pm\large\frac{\sqrt{10}}{2}$$(3\hat i+\hat j)$
answered Dec 2, 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
...