- #1
misogynisticfeminist
- 370
- 0
I do not understand something about cross products. Say,
[tex] \vec A\times \vec B=\vec C=(C_x, C_y, C_z) [/tex]
and,
[tex] \vec C=(A_x \hat x+A_y \hat y+A_z \hat z)\times (B_x \hat x+B_y \hat y+B_z \hat z)[/tex]
but why is this equivalent to
[tex] (A_x B_y - A_y B_x)\hat x \times \hat y + (A_x B_z - A_z B_x) \hat x \times \hat z + (A_y B_z - A_z B_y) \hat y \times \hat z [/tex]
?
Can someone show me how do i get this? Preferbly an algebraic method instead of a geometric one, because I am poor at visualizing stuff.
[tex] \vec A\times \vec B=\vec C=(C_x, C_y, C_z) [/tex]
and,
[tex] \vec C=(A_x \hat x+A_y \hat y+A_z \hat z)\times (B_x \hat x+B_y \hat y+B_z \hat z)[/tex]
but why is this equivalent to
[tex] (A_x B_y - A_y B_x)\hat x \times \hat y + (A_x B_z - A_z B_x) \hat x \times \hat z + (A_y B_z - A_z B_y) \hat y \times \hat z [/tex]
?
Can someone show me how do i get this? Preferbly an algebraic method instead of a geometric one, because I am poor at visualizing stuff.