Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Need solution for RD Sharma Maths Class 12 Chapter 24 Vector Or Cross Product Exercise Very Short Answer Question, question 22.

Need solution for RD Sharma Maths Class 12 Chapter 24 Vector Or Cross Product Exercise Very Short Answer Question, question 22.

Answers (1)

ANSWER:

  0

HINT:

Simplify  \overrightarrow{a}\times \widehat{i}=\widehat{j} and then find \overrightarrow{a}. \widehat{i}

GIVEN:

\overrightarrow{a} is a unit vector

SOLUTION:

\begin{aligned} \text { so }|\vec{a}| &=1 \\ \text { Let, } \vec{a} &=a_{1} \hat{i}+a_{2} \hat{j}+a_{3} \hat{k} \\ \vec{a} \times \hat{i} &=\left|\begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \\ a_{1} & a_{2} & a_{3} \\ 1 & 0 & 0 \end{array}\right| \\ &=\hat{i}(0-0)-\hat{j}\left(0-a_{3}\right)+\hat{k}\left(0-a_{2}\right) \\ \vec{a} \times \hat{i} &=a_{3} \hat{j}-a_{2} \hat{k} \\ \text { Given, } \vec{a} \times \hat{i} &=\hat{j} \\ & \therefore \hat{j}=a_{3} \hat{j}-a_{2} \hat{k} \end{aligned}

i.e.,

0 \hat{i}+\hat{j}+0 \hat{k}=a_{3} \hat{j}-a_{2} \hat{k}+0 \hat{i}

Comparing co-efficient of \widehat{i},\widehat{j}\text{and } \widehat{k}

\begin{aligned} &a_{3}=1 \\ &a_{2}=0 \\ &a_{1}=0 \\ &\therefore \vec{a}=a \hat{i}+0+\hat{k} \\ &\vec{a}=0+\hat{k} \\ &\therefore \vec{a} .=\hat{k} \end{aligned}

\begin{aligned} \text { Now, } \vec{a} \hat{i} &=\hat{k} \hat{i} \\ &=0 \quad[\because \text { Dot product is zero, } \hat{i} \hat{j}=\hat{k} \hat{i}] \end{aligned}

Posted by

infoexpert24

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

DigiLocker, UMANG, IVRS, and other platforms to check CBSE results
anam-khan

How to check CBSE 12th result 2026 using UMANG app?
anam-khan

CBSE 12th Result 2026 (OUT) LIVE: CBSE Class 12 results out on cbse.gov.in, DigiLocker, UMANG

Latest Question