Given vector p.q = modulos of p cross q. wat is the angle b/w p and q and least possible value for p and q

Question

Given vector p.q = modulos of p cross q. wat is the angle b/w p and q and least possible value for p and q

Answer 1

p dot q = pq cos (theta)

p cross q = pq sin(theta)

(When you write this out, make sure to put vector hats on p and q on the left side of the equations, but not on the right, where I just mean the magnitudes of p and q).

So sin(theta) = cos(theta)

theta = arctangent(1)

The lowest positive value of theta would be pi/4.

It really doesn't matter how big p and q are.  Of course, if either of them is zero, then the product is zero and it doesn't matter what the angle is.