Homework Help: Why a timelike vector and a null vector cannot be orthogonal?

1. Jan 23, 2005

crit

Why a timelike vector and a null vector cannot be orthogonal?
Isn't a null vector orthogonal to any vector, by definition? Anyway, each component of a vector is multiplied by zero, so in the end the sum is zero.

2. Jan 23, 2005

dextercioby

Null 4-vector:
$$n^{\mu};n^{2}=:n^{\mu}n_{\mu}=0$$ (1)

Timelike 4-vector:
$$l^{\mu};l^{2}=:l^{\mu}l_{\mu}<0$$ (2)

Prove that
$$l^{\mu}n_{\mu} \neq 0$$(3)

HINT:Use components and the property of the 'cosine' function.

Daniel.

P.S.Esti varza... :yuck:

3. Jan 24, 2005

dextercioby

HINT:'cosine' appears in the expression of the scalar product between those vectors (space components).Pay attention with the metric...

Daniel.