Dot Product confusion (no calculations involved)

[LearninDaMath]

If I take the Dot Product of two vectors, say A and B, I get: AxBx + AyBy + AzBz

And then when I add those terms, I get the magnitude, right?

So when one of those terms are negative, that means I could end up with a negative magnitude?

I thought magnitude had to be positive.

 

[I like Serena]

You get the squared magnitude of a vector if you take the dot product of that vector with itself.
This is always positive (for a non-zero vector).

A dot product between 2 different vectors can be negative.
This indicates that the angle between the vectors is greater than 90 degrees.

 

[LearninDaMath]

You get the squared magnitude of a vector if you take the dot product of that vector with itself.
This is always positive (for a non-zero vector).

A dot product between 2 different vectors can be negative.
This indicates that the angle between the vectors is greater than 90 degrees.

Thanks I like Serena, this cleared up the confusion.

 

[I like Serena]

Cheers!

 

[asteriatic]

The dot product of two vectors, as you correctly stated, is calculated by multiplying the corresponding components of the vectors and then adding them together. This results in a scalar quantity, which is the magnitude of the projection of one vector onto the other. It is important to note that the dot product does not always result in a positive magnitude. In fact, it can be negative if the angle between the two vectors is greater than 90 degrees. This means that the two vectors are pointing in opposite directions and the resulting magnitude is the difference of their lengths. However, the magnitude itself is always positive, regardless of the sign of the dot product. So while a negative dot product may seem confusing, it simply indicates the direction of the vectors in relation to each other.