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Get Answers to all your Questions
Q. 4.7 Given a + b + c + d = 0, which of the following statements are correct:
(a) a, b, c, and d must each be a null vector,
(b) The magnitude of (a + c) equals the magnitude of ( b + d),
(c) The magnitude of a can never be greater than the sum of the magnitudes of b, c, and d,
(d) b + c must lie in the plane of a and d if a and d are not collinear, and in the line of a and d, if they are collinear?
Answers (1)
(a)Incorrect: The sum of three vectors in a plane can be zero. So it is not a necessary condition that all of a,b,c,d should be null vector.
(b) Correct : We are given that a + b + c + d = 0
So, a + b = - (c + d)
Thus magnitude of a + c is equal to the c+d.
(c) Correct :- We have a + b + c + d = 0
b + c + d = - a
So clearly magnitude of a cannot be greater than the sum of the other three vectors.
(d) Correct:- Sum of three vectors is zero if they are coplanar.
Thus, a + b + c + d = 0
or a + (b + c) + d = 0
Hence (b+c) must be coplanar with a and d
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