# Parallel Vectors

The applet below shows two vectors: and , where , for some scalar . You can change vector , by adjusting the sliders for magnitude and direction, and you can change vector by adjusting the slider for .
Play around with the applet for a bit, until you understand the relationships. Then, answer the questions below.

**Question 1:**We will first make vector

**w**a unit vector. The question is, what scalar do we multiply to

**u**, to get a unit vector (in the same direction)?

**a)**What is a unit vector?

**b)**Set the magnitude of

**u**to 2. Then, adjust t, to make

**w**a unit vector. What t value is this?

**c)**Repeat the above process, for various magnitudes of

**u**.

**d)**Hence, if the magnitude of vector

**u**is

**|u|**, write an equation for

**w**, to make

**w**a unit vector in the same direction as

**u**.

**Question 2:**We will now try to generalize this idea. Say we want a vector in the same direction as

**u**, but length k?

**a)**Set the magnitude of

**u**to be 5. Then, adjust t to make

**w**have magnitude 10 (with the same direction as

**u**. What t value is this?

**b)**Repeat the above process, for various magnitudes of

**u**. Also, change the magnitude you want

**w**to be in (instead of 10).

**c)**Hence, if the magnitude of vector

**u**is

**|u|**, write an equation for

**w**, to make

**w**have length k, in the same direction as

**u**.

**Question 3:**We can also extend this, to parallel vectors.

**a)**What does it mean for two vectors to be parallel?

**b)**Hence, if the magnitude of vector

**u**is

**|u|**, write an equation for

**w**, to make

**w**have length k,

**parallel**to

**u**.

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