Question 24 (OR 1st Question) - CBSE Class 12 Sample Paper for 2020 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by Teachoo

For three non-zero vectors a , b and c , prove that

[ (a - b) (b - c) (c - a)] = 0

For non-zero vectors a, b and c, prove [(a - b) (b - c) (c - a)] = 0

Question 24 (OR 1st Question) - CBSE Class 12 Sample Paper for 2020 Boards - Part 2

Question 24 (OR 1st Question) - CBSE Class 12 Sample Paper for 2020 Boards - Part 3

Note : - This is similar to Ex 10.5, 7 (Supplementary) of NCERT – Chapter 10 Class 12

Check the answer here https://www.teachoo.com/7108/2216/Ex-10.5---7-(Supplementary-NCERT)/category/Ex-10.5/

Transcript

Question 24 (OR 1st Question) For three non-zero vectors a , b and c , prove that [ (a - b) (b - c) (c - a)] = 0 [ (a - b) (b - c) (c - a)] = (a - b) (b - c) x (c - a) = (a - b) [ (b x c) - (b x a) - (c x c) + (c x a) (c x c) = [c] [c] sin 0° n = 0 = (a - b). [(b x c) - (b x a) - 0 + (c x a)] = (a - b). [ (b x c) - (b x a) - 0 + (c x a)] = a [ (b x c) - (b x a) + (c x a) -b [(b x c) - (b x a) + (c x a) = a . (b x c) -a . (b x a) + a (c x a) - b (b x c) b (b x a) - b (c x a) = [a, b, c] - [a, b, a] + [a, c, a] - [b, b, c] + [b, b, a] - [ b, c, a] now [ b, b, c] = [c, b, b] = c (b x b) as (b x b) = 0 = c .0 = 0 similarly, [a, b, a] = 0 [b, b, a] = 0 [a,c, a] = 0 = [a, b, c] - 0 + 0 - 0 + 0 - [ b, c, a] = [a, b, c] - [ b, c, a] as [a, b, c] = [c, a, b ] = - [b, c, a] = [a, b, c] - [a, b, c] = 0

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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