Graphical Representation of Cross Product

[jmtome2]

Homework Statement

Show graphically how $$\vec{a}\times\vec{x}=\vec{d}$$ defines a line. $$\vec{a}$$ and $$\vec{d}$$ are constants. $$\vec{x}$$ is a point on the line.

Homework Equations

$$\vec{a}\times\vec{x}=a\cdot x\cdot sin(\theta)\cdot \hat{n}$$

The Attempt at a Solution

Not sure if the included relevant equation is even relevant in this case. In any case, trying to graph this as a line seems impossible. Holding $$\vec{a}$$ constant and varying $$\vec{x}$$ along the line must result in different values of $$\vec{d}$$ which breaks the constraints on the original problem. It seems to me as if the above equation could only have one solution and, therefore, result in a point, not a line.

The only way I see this working is to imply the the above equation has multiple solutions (points along the line). Is this possible? And, if so, could anyone explain it in a simple manner?.

 

[rpf_rr]

It's the line created by the vectors that have their component perpendicular to a equal to x*sin(theta) (it's not exact, the vectors must stay in a certain sense at right of a, if not they created two lines), the vector product is for definition the product of a times the component of the other vector perpendicular to a, times a certain normal vector oriented with the ax of the plane. You can draw it int this way, taken a and x, draw a parallel line to a that passes for x