The properties of vector addition are:
(i) A vector can be added only to a vector.
(ii) Closure property of addition: The sum of two vectors is also a vector. Hence, vectors are closed under addition.
(iii) Vector addition is commutative.
i.e.
(iv)Vector addition is associative.
i.e.
(v) Vector addition is distributive.
i.e.
(vi) Magnitude of the resultant of two vectors is less or equal to the sum of the magnitude of two vectors and greater or equal to the magnitude of the difference of the magnitude of two vectors.
i.e.
At what angle do the two vectors of magnitude A + B and A - B act so that their resultant is ?
The magnitude of the resultant of two vectors acting at angle is given by
Here, P = A + B, Q = A - B
Let two vectors be represented by two adjacent sides OA and OB of parallelogram OACB.
From C draw CD perpendicular to OA produced.
[corresponding angle]
From
Special cases:
Two vectors are represented by the two sides of a parallelogram drawn from point O. Show that the diagonal not passing through O is given by
Let two vectors be represented by two adjacent sides of parallelogram OP and OQ drawn from O as shown in the figure.
Complete the parallelogram OPSQ.
Hence the diagonals not passing through O represent the difference of two vectors.