Question 24 (OR 2nd Question) - CBSE Class 12 Sample Paper for 2020 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards
Last updated at Feb. 21, 2020 by Teachoo

If a + b + c = 0 and |a| = 3, |b| = 5, |c| = 7, then find the value of a.bΒ + b.cΒ + c.a

Note
: - This
is similar to
Example 29 of NCERT β Chapter 10 Class 12

Check the answer here
https://www.teachoo.com/3461/748/Example-29---Let-a---b---c--0--find-a.b---b.c---c.a-if--a---1/category/Examples/

Β

Transcript
Question 24 (OR 2nd Question) if π β + π β + π β = 0 and |π β | = 3, |π β | = 5, |π β | = 7, then find the value of π β. π β + π β. π β + π β. π β .
Given,
π β + π β + π β = 0 β
So, |π β" + " π β" + " π β | = |π β | = 0
Now,
|π β+π β+π β |2
= (π β + π β + π β) . (π β + π β + π β)
= π β. π β + π β . π β + π β . π β + π β . π β + π β . π β + π β . π β + π β . π β + π β . π β + π β . π β
= π β. π β + π β . π β + π β . π β + π β . π β + π β . π β + π β . π β + π β . π β + π β . π β + π β . π β
= π β . π β + π β . π β + π β . π β + 2π β. π β + 2π β. π β + 2π β. π β
= π β . π β + π β . π β + π β . π β + 2(π β. π β + π β. π β + π β. π β)
Prop : π β . π β = |π β |2
= |π β |π + |π β |π + |π β |π + 2 (π β. π β + π β. π β + π β . π β)
= 32 + 52 + 72 + 2(π β. π β + π β. π β + π β. π β)
= 9 + 25 + 49 + 2(π β. π β + π β. π β + π β. π β)
= 83 + 2 (π β. π β + π β. π β + π β. π β)
β΄ |π β+π β+π β|2 = 83 + 2 (π β. π β + π β. π β + π β. π β)
Now,
|π β" + " π β" + " π β | = 0
|π β" + " π β" + " π β |^2 = 0
83 + 2 (π β. π β + π β. π β + π β. π β) = 0
2(π β. π β + π β. π β + π β. π β) = β83
(π β. π β + π β. π β + π β. π β) = (βππ)/π

Show More