Given a+ b + c + d = 0, which of the following statement are correct:(

1.	Given a+ b + c + d = 0, which of the following statement are correct:(a) a, b, c and d must 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 a and d if a and d are not collinear, and in the line of a and d, if they are collinear.
Answer» (a) Incorrect, because a +b +c +d can zero in many ways other than that (vector a,b,c, and d) must each be a null vector. (b) Correct, as (vector a + b + c + d = 0;) (vector a + c) = -( vector b + d). Thus, (vector a + b) is equal to negative of( vector b + d) and hence the statement that magnitude of (vector A + C) is equal to the magnitude of (vector b + d) is correct. (c) correct, Since (vector a + b + c + d = 0') (vector a = -(b + c + d)) Thus, magnitude of vector a is equal to (vector b + c + d). The sum of the magnitude of (vectors b + c) and d may be grater than or equal to that of vector a. Hence the statement that the magnitude of vector a can never be greater than the sum of the magnitude of (vector b, c and d) is correct. (d) Correct, because (vector a +b +c +d = 0;) hence ((vector b + c) + a + d = 0) The resultant sum of three (vectors b + c,+ a+ d) can be zero only if (vector b +c) is in the plane of (vector a and d). In case vector a and d are collnear, (vector b + c) must be the line of (vector a and d.) Hence the given statement is correct.

Given a+ b + c + d = 0, which of the following statement are correct:(a) a, b, c and d must 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 a and d if a and d are not collinear, and in the line of a and d, if they are collinear.

Answer»

(a) Incorrect, because a +b +c +d can zero in many ways other than that (vector a,b,c, and d) must each be a null vector.

(b) Correct, as (vector a + b + c + d = 0;) (vector a + c) = -( vector b + d).

Thus, (vector a + b) is equal to negative of( vector b + d) and hence the statement that magnitude of (vector A + C) is equal to the magnitude of (vector b + d) is correct.

(vector a = -(b + c + d))

Thus, magnitude of vector a is equal to (vector b + c + d). The sum of the magnitude of (vectors b + c) and d may be grater than or equal to that of vector a. Hence the statement that the magnitude of vector a can never be greater than the sum of the magnitude of (vector b, c and d) is correct.

(d) Correct, because (vector a +b +c +d = 0;) hence ((vector b + c) + a + d = 0)

The resultant sum of three (vectors b + c,+ a+ d) can be zero only if (vector b +c) is in the plane of (vector a and d). In case vector a and d are collnear, (vector b + c) must be the line of (vector a and d.) Hence the given statement is correct.

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