Email
logo

Ask Questions, Get Answers

X
 
Questions  >>  CBSE XII  >>  Math  >>  Vector Algebra
Answer
Comment
Share
Q)

If $\overrightarrow{a}=\hat i+\hat j+2\hat k\;and\;\overrightarrow{b}=2\hat i+\hat j-2\hat k,$then find the unit vector in the direction of $\;2\overrightarrow{ a}- \overrightarrow{b}$

1 Answer

Comment
A)
Toolbox:
  • Unit vector in the direction of $\overrightarrow {a}=\large \frac{\overrightarrow {a}}{|\overrightarrow {a}|}$
Let $\overrightarrow{a}=\hat i+\hat j+2\hat k\;and\;\overrightarrow{b}=2\hat i+\hat j-2\hat k,$
Therefore $ 2\overrightarrow{a}-\overrightarrow{b}=2(\hat i+\hat j+2 \hat k)-(2 \hat i+\hat j-2 \hat k)$
$\qquad\qquad \qquad= 2\hat i+2\hat j+4 \hat k-2 \hat i-\hat j+2 \hat k$
Therefore $ 2\overrightarrow{a}-\overrightarrow{b}=\hat j+6 \hat k$
The magnitude of this vector is
$ |2\overrightarrow{a}-\overrightarrow{b}|=\sqrt {(1)^2+6^2}$
$=\sqrt {37}$
Hence the Unit vector in the direction of $|(2 \overrightarrow {a}-\overrightarrow {b})| is =\large \frac{2\overrightarrow {a}-\overrightarrow {b}}{|2\overrightarrow {a}-\overrightarrow {b}|}$
$=\Large\frac{\hat j+6 \hat k}{\sqrt {37}}$
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Continue
Please choose your payment mode to continue
Home Ask Homework Questions
...