Find the area of the triangle whose two sides are represented by the vectors 2i ฬ‚ ๐‘Ž๐‘›๐‘‘ − 3j ฬ‚.

Find area of the triangle whose two sides are vectors 2i and -3j

Question 11 - CBSE Class 12 Sample Paper for 2021 Boards - Part 2

  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Transcript

Question 11 Find the area of the triangle whose two sides are represented by the vectors 2๐‘– ฬ‚ ๐‘Ž๐‘›๐‘‘ โˆ’3๐‘— ฬ‚ We know that Area of triangle ABC = 1/2 |(๐ด๐ต) โƒ— ร— (๐ด๐ถ) โƒ— | Here, (๐ด๐ต) โƒ— = 2๐‘– ฬ‚ and (๐ด๐ถ) โƒ— = โˆ’3๐‘— ฬ‚ (๐‘จ๐‘ฉ) โƒ— ร— (๐‘จ๐‘ช) โƒ— = |โ– 8(๐‘– ฬ‚&๐‘— ฬ‚&๐‘˜ ฬ‚@2&0&0@0&โˆ’3&0)| = ๐‘– ฬ‚ [(0 ร— 0)โˆ’(โˆ’3 ร— 0)] โˆ’ ๐‘— ฬ‚[(2 ร— 0)โˆ’(0 ร— 0)] + ๐‘˜ ฬ‚[(2 ร— โˆ’3)โˆ’(0 ร— 0)] = โˆ’6๐’Œ ฬ‚ Magnitude of (๐ด๐ต) โƒ— ร— (๐ด๐ถ) โƒ— = |โˆ’6๐‘˜ ฬ‚| = 6 So, area of triangle ABC = 1/2 |(๐ด๐ต) โƒ—" ร— " (๐ด๐ถ) โƒ— | = 1/2 ร— 6 = 3 square units

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

About the Author

Davneet Singh's photo - Teacher, Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.