+91-8076753736 support@wiredfaculty.com
logo
logo

NCERT Classes

  • Class 7
  • Class 8
  • Class 9
  • Class 10
  • Class 11
  • Class 12

Previous-Year-Papers

  • CBSE Class 10 and 12
  • NEET Class 12
  • IIT JEE-Main Class 12
  • ICSE Class 10 Class 12
  • CLAT Class 12

Entrance Exams

  • IIT-JEE
  • NEET
  • CLAT
  • SSC-CGL
  • SSC-CHSL

State Boards

  • Assam Board
  • UP Board English Medium
  • Up Board Hindi Medium
  • CBSC Board English Medium
  • CBSC Board Hindi Medium
  • Manipur Board
  • Goa Board
  • Gujrat Board
  • Haryana Board English Medium
  • Haryana Board Hindi Medium
  • Uttarakhand Board English Medium
  • Uttarakhand Board Hindi Medium
  • Himachal Board English Medium
  • Himachal Board Hindi Medium
  • ICSE Board
  • Jharkhand Board English Medium
  • Jharkhand Board Hindi Medium
  • Karnataka Board
  • Meghalya Board
  • Nagaland Board
  • Punjab Board
  • Rajasthan Board English Medium
  • Rajasthan Board Hindi Medium

For Daily Free Study Material Join wiredfaculty

Home > Vector Algebra

Sponsor Area

Vector Algebra

Question
CBSEENMA12034142
Wired Faculty App

Using vectors, prove Cosine formula 
cos space straight C space equals space fraction numerator straight a squared plus straight b squared minus straight c squared over denominator 2 ab end fraction

Solution
Long Answer

Let BC with rightwards arrow on top space equals space straight a with rightwards arrow on top,  CA with rightwards arrow on top space equals straight b with rightwards arrow on top comma space AB with rightwards arrow on top space equals straight c with rightwards arrow on top
therefore space space space BC space equals space straight a comma space space space CA space equals space straight b comma space space space AB space equals space straight c
Now, straight a with rightwards arrow on top plus straight b with rightwards arrow on top equals negative straight c with rightwards arrow on top
rightwards double arrow space space space left parenthesis straight a with rightwards arrow on top plus straight b with rightwards arrow on top right parenthesis squared space equals space left parenthesis negative straight c with rightwards arrow on top right parenthesis squared
rightwards double arrow space space space space straight a with rightwards arrow on top squared plus straight b with rightwards arrow on top squared space plus space 2 space straight a with rightwards arrow on top space straight b with rightwards arrow on top space equals space straight c with rightwards arrow on top squared
rightwards double arrow space space straight a squared plus straight b squared plus 2 space ab space cos left parenthesis 180 degree space minus space straight C right parenthesis space equals space straight c squared
rightwards double arrow space space space straight a squared plus straight b squared minus 2 space ab space cos space straight C space equals space straight c squared
rightwards double arrow space space straight a squared plus straight b squared minus 2 space ab space cos space straight C space equals straight c squared space space space space space space space space space space rightwards double arrow space space space space 2 space ab space cos space straight C space equals space straight a squared plus straight b squared minus straight c squared
rightwards double arrow space space cos space straight C space equals space fraction numerator straight a squared plus straight b squared minus straight c squared over denominator 2 space straight a space straight b end fraction


  • Bookmark
  • Facebook
  • WhatsApp
  • Twitter
  • Linkedin
  • Copy Link
  • twitter button
  • facebook logo
  • watsapp logo

Some More Questions From Vector Algebra Chapter

Classify the following measures as scalars and vectors.
(i) 5 seconds
(ii) 1000 cm3
(iii) 10 Newton
(iv) 30 km hr
(v) 10 g/cm3
(vi) 20 m/s towards north

Classify the following measures as scalars and vectors.
10 kg

Classify the following measures as scalars and vectors.
2 meters north-west

Classify the following measures as scalars and vectors.
40°

Classify the following measures as scalars and vectors.
40 watt

Classify the following measures as scalars and vectors.
10–19 coulomb

Classify the following measures as scalars and vectors.
20 m/s2

Classify the following measures as scalars and vectors.
time period

Classify the following measures as scalars and vectors.
distance

Classify the following measures as scalars and vectors.
force

Mock Test Series

Mock Test Series

  • NEET Mock Test Series
  • IIT-JEE Mock Test Series
  • CLAT Mock Test Series
  • SSC-CGL Mock Test Series
  • SSC-CHSL Mock Test Series

NCERT Sample Papers

  • CBSE English Medium
  • CBSE Hindi Medium
  • ICSE

Entrance Exams Preparation

  • NEET
  • IIT-JEE
  • CLAT
  • SSC-CGL
  • SSC-CHSL

ABOUT US

  • Company
  • Term of Use
  • Privacy Policy

NCERT SOLUTIONS

  • NCERT Solutions for Class-8th
  • NCERT Solutions for Class-9th
  • NCERT Solutions for Class-10th
  • NCERT Solutions for Class-11th
  • NCERT Solutions for Class-12th

CONTACT US

Phone Number

+91-8076753736

Email Address

support@wiredfaculty.com

Loaction

A2/44 Sector-3 Rohini Delhi 110085

Copyright © 2025 wiredfaculty. Powered by -wiredfaculty.com