Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Let <img alt="\overrightarrow{\mathrm{a}}=5 \hat{\mathrm{i}}-\hat{\mathrm{j}}-3 \mathrm{k}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Coverrightarrow%7B%5Cmathrm%7Ba%7D%7D%3D5%20%

Let \overrightarrow{\mathrm{a}}=5 \hat{\mathrm{i}}-\hat{\mathrm{j}}-3 \mathrm{k} and \overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+3 \hat{\mathrm{j}}+5 \mathrm{k} be two vectors. Then which one of the following statements is TRUE ?

Option: 1

Projection of \vec{a} on \vec{b} is \frac{17}{\sqrt{35}} and the direction of the projection vector is same as of \vec{b}.


Option: 2

Projection of \vec{a} on \vec{b} is \frac{17}{\sqrt{35}} and the direction of the projection vector is opposite to the direction of \vec{b}. 

 


Option: 3

Projection of \vec{a} on \vec{b} is \frac{17}{\sqrt{35}} and the direction of the projection vector is same as of \vec{b}.


Option: 4

Projection of \vec{a} on \vec{b} is \frac{17}{\sqrt{35}}  and the direction of the projection vector is opposite to the

direction of  \vec{b}


Answers (1)

best_answer

\text { Projection of } \vec{a} \text { on } \vec{b}=\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}

\begin{aligned} & \Rightarrow \frac{(5 \hat{\imath}-\hat{j}-3 \hat{k}) \cdot(\hat{\imath}+3 \hat{j}+5 \hat{k})}{\sqrt{1^2+3^2+5^2}}=\frac{5-3-15}{\sqrt{35}} \\ & \Rightarrow \frac{-13}{\sqrt{35}} \end{aligned}

Posted by

vinayak

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2025 Session 2 City Slip (OUT) Live: NTA exam city intimation slip link available; admit card date
anam-khan

AESL expands Aakash Digital 2.0 to offer AI-powered coaching for NEET, JEE, Olympiads
anam-khan

Bihar Board extends BSEB Super 50 free coaching application last date to March 26

Latest Question