- #1
doctorjuice
- 7
- 0
First question:
a x b = -b x a
Why is this so?
As I understand, a major purpose of the cross product (if not, the purpose) is to find a third vector that is perpendicular to two other vectors simultaneously. Let's say a x b = c. Shouldn't the answer really be, a x b = +/- c? Since, of course, both c and -c are perpendicular to a and b simultaneously.
The situation of the sqrt(4) = +/- 2 is analogous to this.
Second question:
The cross product is said to be something that only works in 3 dimensional space. In 2D, it is said to be not applicable. Take two vectors in 2D that are just the negative of each other. Obviously a line can be drawn straight up relative to these two vectors that is perpendicular to both (visualize an upside down T). Since the cross product's main purpose is to find a third vector that is perpendicular to two other vectors, can it be said that the cross product fails in 2 dimensional space?
Thanks for your time.
a x b = -b x a
Why is this so?
As I understand, a major purpose of the cross product (if not, the purpose) is to find a third vector that is perpendicular to two other vectors simultaneously. Let's say a x b = c. Shouldn't the answer really be, a x b = +/- c? Since, of course, both c and -c are perpendicular to a and b simultaneously.
The situation of the sqrt(4) = +/- 2 is analogous to this.
Second question:
The cross product is said to be something that only works in 3 dimensional space. In 2D, it is said to be not applicable. Take two vectors in 2D that are just the negative of each other. Obviously a line can be drawn straight up relative to these two vectors that is perpendicular to both (visualize an upside down T). Since the cross product's main purpose is to find a third vector that is perpendicular to two other vectors, can it be said that the cross product fails in 2 dimensional space?
Thanks for your time.