Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain solution RD Sharma class 12 Chapter 23 Scalar or Dot Products Exercise Very Short Answer question 9

Explain solution RD Sharma class 12 Chapter 23 Scalar or Dot Products Exercise Very Short Answer question 9

Answers (1)

best_answer

ANSWER:  \vec{a} \& \vec{b}  are perpendicular

GIVEN:  |\vec{a}+\vec{b}|=|\vec{a}|-|\vec{b}|

HINTS: Use the identity of  (a+b)^{2} \&(a-b)^{2}

SOLUTION:

\begin{aligned} &|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}| \\ & \end{aligned}

(|\vec{a}+\vec{b}|)^{2}=(|\vec{a}-\vec{b}|)^{2}\qquad[\text { Squaring both sides }]

\begin{aligned} &\Rightarrow|\vec{a}|^{2}+|\vec{b}|^{2}+2 \vec{a} \cdot \vec{b}=|\vec{a}|^{2}+|\vec{b}|^{2}-2 \vec{a} \cdot \vec{b}\qquad\left[\because(\mathrm{a}+\mathrm{b})^{2}=\mathrm{a}^{2}+b^{2}-2 a b \&(\mathrm{a}-\mathrm{b})^{2}=\mathrm{a}^{2}+b^{2}-2 a b\right] \\ & \end{aligned}

\Rightarrow 2 \vec{a} \cdot \vec{b}=-2 \vec{a} \cdot \vec{b} \\

\Rightarrow \vec{a} \cdot \vec{b}=-\vec{a} \cdot \vec{b} \\

\Rightarrow \vec{a} \cdot \vec{b}+\vec{a} \cdot \vec{b}=0 \Rightarrow 2 \vec{a} \cdot \vec{b}=0

\therefore \vec{a} is perpendicular to  \vec{b}

Posted by

infoexpert27

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

CBSE question papers QR codes part of 'internal systems'; board cautions 'unverified claims'
anam-khan

Delhi court grants interim bail to Class 12 student in stabbing case to appear for CBSE exam
anam-khan

CBSE Class 12 History Exam 2026 Analysis: Moderate paper, tricky MCQs, student-friendly pattern

Latest Question