Question

why is the cross product of 2 parallel vectors always 0? How can it be determined that a × b = |a| |b| sin(θ) n from the other formula

• c_x = a_yb_z − a_zb_y
• c_y = a_zb_x − a_xb_z
• c_z = a_xb_y − a_yb_x

Answer 1

Cross product means the area of the parallelogram formed by two vector as the adjacent sides now if these are parallel then area = 0 thus cross product is zero

Now a*b = absin(angle)

For a and b being parallel , angle = 0

Thus a*b = 0

Now a*b = absin(angle) let angle be A let a be a vector along x axis , b be vector at an angle A to it now the n will be in z direction

So the cross will be in z direction

We are given the z component as

Cz = axby-aybx

Here ax = a , bx = bcosA , ay=0 and by= bsinA

Thus Cz = absinA -0

Hence this formula can be obtained like above