Given a + b + c + d = 0 which of the following statement is incorrect

Easy

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 b if a and d are not collinear, and in the line of a and d, if they are collinear

Solution

(a) Incorrect : For $\large \overline a + \overline b + \overline c + \overline d = \overline 0$ It is not necessary that $\large \overline a = \overline b = \overline c = \overline d = \overline 0$
(b) correct : As $\large \overline a + \overline b + \overline c + \overline d = \overline 0$
$\large (\bar a + \bar c) = - (\bar b + \bar d) \Rightarrow \left| {\overline a + \overline c } \right| = \left| {\overline b + \overline d } \right|$
(c) correct : $\large \overline a = - (\overline b + \overline c + \overline d );\left| {\overline a } \right| = \left| {\overline b + \overline c + \overline d } \right|$
(d) correct : As $\large \overline a + \overline b + \overline c + \overline d = \overline 0$
$\large (\overline b + \overline c ) + \overline a + \overline d = 0;\overline a + \overline d = - (\overline b + \overline c )$

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