# Thread: Finding vectors of give magnitude that are perpendicular...

1. ## Finding vectors of give magnitude that are perpendicular...

Hi guys,

Just beginning vectors but I am still not grasping the concept that well, I have looked around a bit and tried a few ideas out...

The question is
Let v = (4, 2). Find all vectors of magnitude 4 that are perpendicular to v.

Not entirely sure how to approach this... pretty awful with vectors, I calculated the magnitude of v (root 20), however I really wasn't sure what to do with that afterwards.. any help would be much appreciated.

Sim

2. ## Re: Finding vectors of give magnitude that are perpendicular...

Originally Posted by simwun
Hi guys,

Just beginning vectors but I am still not grasping the concept that well, I have looked around a bit and tried a few ideas out...

The question is
Let v = (4, 2). Find all vectors of magnitude 4 that are perpendicular to v.

Not entirely sure how to approach this... pretty awful with vectors, I calculated the magnitude of v (root 20), however I really wasn't sure what to do with that afterwards.. any help would be much appreciated.

Sim
1. Let $\displaystyle \vec p$ denotes the perpendicular vector of $\displaystyle \vec v$

2. Since $\displaystyle \vec v \perp \vec p ~\implies~\vec v \cdot \vec p = 0$

You'll get $\displaystyle \overrightarrow{p_1} = \langle -2, 4 \rangle$ or $\displaystyle \overrightarrow{p_2} = \langle 2, -4 \rangle$

3. These vectors have still the magnitude $\displaystyle \sqrt{20} = 2 \sqrt{5}$

You are looking for a factor f such that

$\displaystyle f \cdot 2 \sqrt{5} = 4$

Determine f.

3. ## Re: Finding vectors of give magnitude that are perpendicular...

Ah i see, cheers mate