Email
Chat with tutor
logo

Ask Questions, Get Answers

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

If $A,B,C,D$ are the points with position vectors $\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k},2\overrightarrow{i}+\overrightarrow{j}+3\overrightarrow{k},2\overrightarrow{i}-3\overrightarrow{k},3\overrightarrow{i}+2\overrightarrow{i}+\overrightarrow{k},$ respectively ,find the projection of $\overrightarrow{AB}$ along $\overrightarrow{CD}.$

$\begin{array}{1 1} 3 \\ \sqrt 3 \\ 9 \\ 27 \end{array} $

1 Answer

Comment
A)
Toolbox:
  • Projection of $ \overrightarrow a \: along \: \overrightarrow b\: is \: \large\frac{\overrightarrow a.\overrightarrow b}{|\overrightarrow b|} $
Given $\overrightarrow{OA}=\hat i+\hat j+\hat k$, $\overrightarrow{OB}=2\hat i+\hat j+3\hat k$, $\overrightarrow{OC}=2\hat i-3\hat k$ and $\overrightarrow{OD}=3\hat i+2\hat j+\hat k$
Let us determine $ \overrightarrow{AB}$ and $ \overrightarrow{CD}$
$ \overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}$
$\qquad=(2\hat i+\hat j+3\hat k)-(\hat i+\hat j+\hat k)$
$\qquad=\hat i+2\hat k$
$ \overrightarrow{CD}=\overrightarrow{OD}-\overrightarrow{OC}$
$\qquad=(3\hat i+2\hat j+\hat k)-(2\hat i-3\hat k)$
$\qquad=\hat i+2\hat j+ 4 \hat k$
Projection of $ \overrightarrow {AB} $ along $ \overrightarrow {CD}$ is
$\large\frac{\overrightarrow {AB}.\overrightarrow {CD}}{|\overrightarrow {CD}|} =\large\frac{(\hat i+2 \hat k).(\hat i+2 \hat j +4 \hat k)}{\sqrt {1^2+2^2+(-2)^2}}$
$=\large\frac{1+8}{\sqrt {1+4+4}}=\frac{9}{3}$
$=3$
Hence the projection of $ \overrightarrow{AB} \: along \: \overrightarrow{CD}$ is 3
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
Your payment for is successful.
Continue
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.
...