Vector orientation versus infinite line

Perpendicular vector

Orthogonal vector

Parallel vector

Vector name

$A$

$B$

$C$

Vector norm

$\Vert A\Vert =\Vert B\Vert =\Vert C\Vert =\left|U/r\right|$

Square Root Cross product with positive source

Physical field value

(U/m)

U/r

U/r

U/r

Orthogonality

When U > 0

$A={\left(B\wedge C\right)}^{1/2}$

$B={\left(C\wedge A\right)}^{1/2}$

$C={\left(A\wedge B\right)}^{1/2}$

Square Root Cross product with negative source

Physical field value

(U/m)

−U/r

−U/r

−U/r

Orthogonality

When U < 0

$A=-{\left(B\wedge C\right)}^{1/2}$

$B=-{\left(C\wedge A\right)}^{1/2}$

$C=-{\left(A\wedge B\right)}^{1/2}$