﻿ Given a + b+ c + d = 0, which of the following statementsare 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 ? from Physics Motion in A Plane Class 11 Manipur Board

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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 ?

a)

Incorrect

In order to make vectors a + b + c + d = 0, it is not necessary to have all the four given vectors to be null vectors. There are many other combinations which can give the sum zero.

(b)

Correct

a + b + c + d = 0

a + c = – (b + d)

Taking modulus on both the sides, we get,

| a + c | = | –(b + d)| = | b + d |

Hence, the magnitude of (a + c) is the same as the magnitude of (b + d).

(c)

Correct

a + b + c + d = 0

a = - (b + c + d)

Taking modulus both sides, we get,

| a | = | b + c + d |

| a | ≤ | a | + | b | + | c | ... (i)

Equation (i) shows that the magnitude of a is equal to or less than the sum of the magnitudes of b, c, and d.

Hence, the magnitude of vector a can never be greater than the sum of the magnitudes of b, c, and d.

(d)

Correct

For a + b + c + d = 0

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