If C→=A→+B→ then

If C⇀=A⇀+B⇀Then maximum value of C⇀=A⇀+B⇀ and minimum value of C⇀=A⇀-B⇀So it is possible that C can have a value less thanA⇀or less than B⇀

If C→=A→+B→ then

If C⇀=A⇀+B⇀Then maximum value of C⇀=A⇀+B⇀ and minimum value of C⇀=A⇀-B⇀So it is possible that C can have a value less thanA⇀or less than B⇀

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If $\vec{C} = \vec{A} + \vec{B}$ then

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It is possible to have $|\vec{C}| < |\vec{A}| and |\vec{C}| < |\vec{B}|$

$\vec{C}$ is always greater than $|\vec{A}|$

C is always equal to A+B

C is never equal to A+B

answer is D.

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Detailed Solution

$If \overset{⇀}{C} = \overset{⇀}{A} + \overset{⇀}{B}$

$Then maximum value of |\overset{⇀}{C}| = |\overset{⇀}{A}| + |\overset{⇀}{B}| and minimum value of |\overset{⇀}{C}| = |\overset{⇀}{A}| - |\overset{⇀}{B}|$
$So it is possible that C can have a value less than |\overset{⇀}{A}| or less than |\overset{⇀}{B}|$