Condition for Parallel Vectors: Determinant Method

[abrowaqas]

Homework Statement

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..

Homework Equations

A*B=AB sin(theeta)

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.

 

[hgfalling]

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

 

[Mark44]

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

 

[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
$$\frac{A_1}{B_1}= \frac{A_2}{B_2}= \frac{A_3}{B_3}$$

 

[abrowaqas]

thank you hall

 

[HallsofIvy]

Well, I just said what Mark44 said!