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

Posted on April 22, 2020 by user

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

$\underset{˜}{a} and \underset{˜}{b}$ are not parallel and

$(k - 7) \underset{˜}{a} = (5 + h) \underset{˜}{b}$ , find the value of k and of h.

Solution:

The vectors

$\underset{˜}{a} and \underset{˜}{b}$ are not parallel, so

k – 7 = 0 → k = 7

5 + h = 0 → h = –5