Home
Class 12
MATHS
If vec a, vec b and vec c be any three ...

If ` vec a, vec b and vec c` be any three vectors then show that ` vec a + ( vec b + vec c) = ( vec a + vec b) + vec c`

Text Solution

AI Generated Solution

To prove that \(\vec{a} + (\vec{b} + \vec{c}) = (\vec{a} + \vec{b}) + \vec{c}\), we will use the properties of vector addition. ### Step-by-Step Solution: 1. **Define the Vectors**: Let \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\) be any three vectors in a vector space. 2. **Consider the Left Side**: We start with the left-hand side of the equation: \[ ...
Promotional Banner

Similar Questions

Explore conceptually related problems

If a, b and c are any three vectors, then prove that vec a.(vec b+vec c)=(vec a.vec b)+(vec a.vec c)

If vec a, vec b , vec c are three non- coplanar vectors such that vec a + vec b + vec c = alpha vec d and vec b +vec c + vec d = beta vec a, " then " vec a + vec b + vec c + vec d to equal to

Let vec a, vec b, vec b, vec b are three vectors such that vec a * vec a = vec b * vec b = vec c * vec c = 3 and | vec a-vec b | ^ (2) + | vec b-vec c | ^ (2) + | vec c-vec a | ^ (2) = 27 then

Let vec a , vec b , vec c are three vectors , such that vec a + vec b + vec c = vec 0 .If , |vec a|=3 , |vec b|=4 and | vec c|=5 , then the value of, |vec a+vec b|^(2) + |vec b-vec c|^(2) + |vec c+vec a|^(2) , equal to :

(vec a xxvec b)xxvec c=vec a xx(vec b xxvec c), Where vec a,vec b and vec c and any three vectors such that vec a*vec b=0,vec b*vec c=0 then vec a and vec c are

If (vec avec b) xxvec c = vec a xx (vec a xxvec c), where vec a, vec b, vec c are any three vectors such that vec a * vec b! = 0 and vec b.vec c! = 0 then vec a and vec c are

If vec a, vec b, vec c are three vectors such that | vec b | = | vec c | then {(vec a + vec b) xx (vec a + vec c)} xx {(vec b xxvec c)} * (vec b + vec c) =

If vec a,vec b, and vec c are three vectors such that vec a xxvec b=vec c,vec b xxvec c=vec a,vec c xxvec a=vec b then prove that |vec a|=|vec b|=|vec c|

If vec a, vec b and vec c are non coplaner vectors such that vec b xxvec c = vec a, vec c xxvec a = vec b and vec a xxvec b = vec c then | vec a + vec b + vec c | =

If vec a, vec b, vec c are unit vectors such that vec a + vec b + vec c = vec 0 find the value of vec a * vec b + vec b * vec c + vec c * vec avec a * vec b + vec b * vec c + vec c * vec a