Dots and Blues!

Geometry Level 2

Three vectors $\vec{a}, \vec{b}$ and $\vec{c}$ in $\mathbb{R}^{3}$ satisfy the following equation:

$\vec{a} \cdot \vec{b} = \vec{c} \cdot \vec{b}.$

What can you deduce about $\vec{a}$ and $\vec{c}$ from this information?

\vec{a} \parallel \vec{c}

\vec{a} \perp \vec{c}

\left \| \vec{a} \right \| = \left \| \vec{c} \right \|

None of the above

1 solution

Atomsky Jahid
Jan 18, 2017

Relevant wiki: Dot Product

As you can see from the above picture, the vectors $\vec{a}$ and $\vec{c}$ don't need to be parallel or perpendicular. And, they also don't need to have equal norm or magnitude.

I've never seen the notation used in the first option and I couldn't easily figure out what it means:

https://en.wikipedia.org/wiki/Vertical_bar#Mathematics

Got me a little bit confused.

Niklas Gruhn - 1 year, 4 months ago

Do you have any problem with the notations now?

Atomsky Jahid - 1 year, 4 months ago

I guess it means a and b are parallel . Retrospectively, it's kind of obvious but I think that's typical in math. Once you understand it you don't understand how you once couldn't understand it.

Niklas Gruhn - 1 year, 4 months ago

Dots and Blues!

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