Two vectors to be parallel

1. Aug 5, 2010

abrowaqas

1. The problem statement, all variables and given/known data
What is the condition of two vectors to be parallel?
if A= A1i+A2j+A3k and B=B1i+B2j+B3k then what is the condition that the two vectors are parallel..

2. Relevant equations

A*B=AB sin(theeta)

3. The attempt at a solution

by cross product i find the condition
A1/B1=A2/B2=A3/B3 .... under which determinant becomes equal to to 0. which is the condition for parallel..theeta = 0 so sin 0 = 0 ... kindly confirm is it write or wrong.

2. Aug 5, 2010

hgfalling

Two vectors are parallel if their cross product is the zero vector.

3. Aug 5, 2010

Staff: Mentor

Also, two vectors are parallel if either is a constant multiple of the other.

4. Aug 6, 2010

HallsofIvy

Specifically, $A_1\vec{i}+ A_2\vec{j}+ A_3\vec{k}$ and $\B_1\vec{i}+ B_2\vec{j}+ B_3\vec{k}$ are parallel if and only if
$$\frac{A_1}{B_1}= \frac{A_2}{B_2}= \frac{A_3}{B_3}$$

5. Aug 6, 2010

abrowaqas

thank you hall

6. Aug 8, 2010

HallsofIvy

Well, I just said what Mark44 said!