When Is the Projection of a Vector Undefined or Zero?

• emma3001
In summary, the projection of vector a onto vector b can equal 0 if a is perpendicular to b, and it will be undefined if vector b has a length of 0. The formula for the scalar projection of a onto b is [tex]\frac{\vec{a}\cdot\vec{b}}{||b||}[/itex], and it will result in 0 or undefined depending on the values of a and b.
emma3001
I was wondering if it is possible, in projections, to have a projected onto b equal to zero or undefined. In other words, when does a projected onto b equal zero and when is it undefined?

It is certainly possible, in fact common, to have the projection of vector a onto vector b equal to 0: as long as a is perpendicular to b.

The "projection of a onto b" would be "undefined" if b itself has length 0.

In general, the (scalar) projection of a on b is
[tex]\frac{\vec{a}\cdot\vec{b}}{||b||}[/itex]
That's 0 if the dot product of a and b is 0 (a is perpendicular to b) and undefined if ||b||= 0.

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2. How is a projections of vectors inquiry conducted?

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Projections of vectors inquiry can benefit society by providing a deeper understanding of natural phenomena and allowing for the development of new technologies and solutions. It can also help in problem-solving and decision-making in various industries, leading to advancements and improvements in daily life.

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