Mathematics for IGCSE & O level - Vectors (Section 1 - No. 12)
Which of the following is a correct property of vector addition?
Vector addition is commutative (\(\vec{a} + \vec{b} = \vec{b} + \vec{a}\)).
Vector addition is associative (\((\vec{a} + \vec{b}) + \vec{c} = \vec{a} + (\vec{b} + \vec{c})\)).
The magnitude of \(\vec{a} + \vec{b}\) is always equal to the sum of magnitudes of \(\vec{a}\) and \(\vec{b}\).
The sum of a vector and its negative is always the zero vector.
Explanation
Vector addition is commutative and associative. The sum of a vector and its negative results in the zero vector. The magnitude of a + b is only equal to the sum of the magnitudes when vectors are in the same direction
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