How do you find a vector perpendicular to a given vector?

Answer 1

Given vectors A and B, the cross product C is defined as the vector that

1) is perpendicular to both A and B (which is what you are looking for)

2) whose magnitude is the product of the magnitudes of A and B times the sine of the angle between them.

If we write the three elements of A as A(1) A(2) A(3), and the same for B, then the components of C are

C(1)=A(2)*B(3)-A(3)*B(2);

C(2)=A(3)*B(1)-A(1)*B(3);

C(3)=A(1)*B(2)-A(2)*B(1);

Answer 2

Be

u - vector number one

v - vector number two

u is perpendicular to v when

the norm of u times the norm of v times cosine of the angle between the two vectors = 0.