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

**1.**When a vector $\underset{\u02dc}{a}$ is multiplied by a scalar

*k*, the product is $k\underset{\u02dc}{a}$ . Its magnitude is

*k*times the magnitude of the vector $\underset{\u02dc}{a}$ .

**2.**The vector $\underset{\u02dc}{a}$ is

**parallel**to the vector $\underset{\u02dc}{b}$ if and only if $\underset{\u02dc}{b}=k\underset{\u02dc}{a}$ , where

*k*is a constant.

**3.**If the vectors $\underset{\u02dc}{a}$ and $\underset{\u02dc}{b}$ are

**not parallel**and $h\underset{\u02dc}{a}=k\underset{\u02dc}{b}$ , then

*h*= 0 and

*k =*0.

**Example 1:**

If vectors
$\underset{\u02dc}{a}\text{and}\underset{\u02dc}{b}$
are not parallel and
$\left(k-7\right)\underset{\u02dc}{a}=\left(5+h\right)\underset{\u02dc}{b}$
, find the value of

*k*and of*h*.

Solution:Solution:

The vectors
$\underset{\u02dc}{a}\text{and}\underset{\u02dc}{b}$
are not parallel, so

*k*– 7 = 0 →

*k*= 75 +

*h*= 0 →

*h*= –5