Examples of cross product :
i) Angular momentum \(
\mathop L\limits^ \to = \mathop r\limits^ \to \times \mathop P\limits^ \to
\)
ii) Linear velocity \(
\mathop V\limits^ \to = \mathop \omega \limits^ \to \times \mathop r\limits^ \to
\)
iii) Torque \(
\mathop \tau \limits^ \to = \mathop r\limits^ \to \times \mathop F\limits^ \to
\)
iv) Torque on a magnet \(
\mathop \tau \limits^ \to = \mathop M\limits^ \to \times \mathop B\limits^ \to
\)
v) Force on a conductor \(
\mathop F\limits^ \to = i\left( {\mathop l\limits^ \to \times \mathop B\limits^ \to } \right)
\)
vi) Force on a charge \(
\mathop F\limits^ \to = q\left( {\mathop v\limits^ \to \times \mathop B\limits^ \to } \right)
\)
vii) Torque on a coil \(
\mathop \tau \limits^ \to = i\left( {\mathop A\limits^ \to \times \mathop B\limits^ \to } \right)
\)
viii) A force \(
\vec F
\) acts at P and is \(
\vec \tau
\) torque produced about Q. If position vector of P is \(
\overrightarrow {r_1 }
\)and position vector of Q is \(
\overrightarrow {r_2 }
\) then \(
\overrightarrow \tau = \vec r\,x\,\vec F = \left( {\overrightarrow {r_2 } - \overrightarrow {r_1 } } \right)x\vec F
\) .