# 4.2 Multiplication of Vector by a Scalar and the Parallel Condition of Two Vectors

4.2 Multiplication of Vector by a Scalar and the Parallel Condition of Two Vectors
1. When a vector $\underset{˜}{a}$ is multiplied by a scalar k, the product is $k\underset{˜}{a}$ . Its magnitude is k times the magnitude of the vector $\underset{˜}{a}$ .

2. The vector $\underset{˜}{a}$ is parallel to the vector $\underset{˜}{b}$ if and only if $\underset{˜}{b}=k\underset{˜}{a}$ , where k is a constant.

3. If the vectors $\underset{˜}{a}$ and $\underset{˜}{b}$ are not parallel and $h\underset{˜}{a}=k\underset{˜}{b}$ , then h = 0 and k = 0.

Example 1:
If vectors  are not parallel and $\left(k-7\right)\underset{˜}{a}=\left(5+h\right)\underset{˜}{b}$ , find the value of k and of h.

Solution:
The vectors are not parallel, so
k – 7 = 0 → k = 7
5 + h = 0 → h = –5