logo

Ask Questions, Get Answers

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

Find a vector in the direction of vector $5\hat i − \hat j + 2\hat k$ which has magnitude $8$ units.

$\begin{array}{1 1}(A) \large\frac{40}{\sqrt {30}}\hat i-\large\frac{8}{\sqrt 30}\hat j+\large\frac{16}{\sqrt 30}\hat k \\ (B) \large\frac{20}{\sqrt {30}}\hat i-\large\frac{4}{\sqrt 30}\hat j+\large\frac{8}{\sqrt 30}\hat k \\ (C) \large\frac{40}{\sqrt {30}}\hat i+\large\frac{8}{\sqrt 30}\hat j-\large\frac{16}{\sqrt 30}\hat k\\(D) \large\frac{40}{\sqrt {30}}\hat i-\large\frac{8}{\sqrt 30}\hat j-\large\frac{16}{\sqrt 30}\hat k \end{array} $

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • Unit vector in the direction of $\overrightarrow a$ is $\hat a=\large\frac{\overrightarrow a}{|\overrightarrow a|}$
  • If a vector of magnitude k is acting in the direction of $\overrightarrow a$,then it is given by $k.\large\frac{\overrightarrow a}{|\overrightarrow a|}$
Step 1:
Given vector is $5\hat i-\hat j+2\hat k$.
It has magnitude 8 units.
Let $\overrightarrow a=5\hat i-\hat j+2\hat k$
Let us find the magnitude of $\overrightarrow a$.
$|\overrightarrow a|=\sqrt{5^2+(-1)^2+2^2}$
$\quad\;\;=\sqrt{25+1+4}$
$\quad\;\;=\sqrt{30}$
Step 2:
Therefore the unit vector in the direction of $\overrightarrow a$ is $\hat a=\large\frac{\overrightarrow a}{|\overrightarrow a|}$
$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad\;\;=\large\frac{(5\hat i-\hat j+2\hat k)}{\sqrt {30}}$
Step 3:
The vector of magnitude 8 in the direction of vector $\overrightarrow a=8\times$unit vector of $\overrightarrow a $
We know that $\hat a=\large\frac{(5\hat i-\hat j+2\hat k)}{\sqrt {30}}$
The vector of magnitude 8 in the direction of vector $\overrightarrow a=8\times \large\frac{(5\hat i-\hat j+2\hat k)}{\sqrt {30}}$
$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad\quad\;\;\;=\large\frac{8}{\sqrt {30}}$$(5\hat i-\hat j+2\hat k)$
$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad\quad\;\;\;=\large\frac{40}{\sqrt {30}}$$\hat i-\large\frac{8}{\sqrt 30}$$\hat j+\large\frac{16}{\sqrt 30}$$\hat k$
answered May 22, 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
...