VECTOR SCALAR MULTIPLE

The magnitude is always a positive value, so the magnitude of the scalar multiple is the absolute value of the scalar times the magnitude of the original vector. This can be written as ||kv|| = |k| ||v||. The direction of the vector scalar multiple will depend on the sign of the scalar. The following information will help to determine the direction of the scalar multiple of a vector. 

ADDING MULTIPLE VECTORS

If the magnitude and direction of vectors u and v are given in a table, then to find the magnitude and direction of u + v:

1) Determine the horizontal and vertical components for each vector. 

2) Find the sum of the vectors using the horizontal and vertical components of each vector. 

3) Find the magnitude of the sum of the vectors. 

4) Find the direction of the sum of the vectors.