Let the angle between two non zero vectors A(vector) and B(vector ) be 120(degrees) and its resultant be C(vector). Then which of the following is(are) correct?

Question

(a)C must be equal to |A-B|
(b)C must be less than |A-B|
(c) C must be greater than |A-B|
(d) C may be equal to |A-B|

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Answer 1 · 2018-06-12T14:07:24

Option (b)

#bb A * bb B = abs bbA abs bbB cos (120^o) = -1/2 abs bbA abs bbB #

#bbC = bbA + bbB#

#= A^2 + B^2 + 2 bbA * bb B #

# = A^2 + B^2 - abs bbA abs bbB qquad square#

#= (bbA - bbB)*(bbA - bbB)#

#= A^2 + B^2 - 2bbA*bbB #

#= A^2 + B^2 + abs bbA abs bbB qquad triangle#

#abs(bbA - bbB)^2 - C^2= triangle - square = 2 abs bbA abs bbB#

#:. C^2 lt abs(bbA - bbB)^2, qquad bbA, bbB ne bb0#

#:. abs bb C lt abs(bbA - bbB)#