Condition for Parallel Vectors: Determinant Method

In summary, the condition for two vectors to be parallel is that their cross product is equal to the zero vector, or that one is a constant multiple of the other. Specifically, if vector A is equal to A1i + A2j + A3k and vector B is equal to B1i + B2j + B3k, then they are parallel if and only if A1/B1 = A2/B2 = A3/B3.
  • #1
abrowaqas
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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.
 
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  • #2
Two vectors are parallel if their cross product is the zero vector.
 
  • #3
Also, two vectors are parallel if either is a constant multiple of the other.
 
  • #4
Specifically, [itex]A_1\vec{i}+ A_2\vec{j}+ A_3\vec{k}[/itex] and [itex]\B_1\vec{i}+ B_2\vec{j}+ B_3\vec{k}[/itex] are parallel if and only if
[tex]\frac{A_1}{B_1}= \frac{A_2}{B_2}= \frac{A_3}{B_3}[/tex]
 
  • #5
thank you hall
 
  • #6
Well, I just said what Mark44 said!
 

1. What does it mean for two vectors to be parallel?

When two vectors are parallel, it means that they have the same direction or are pointing in the same direction. This indicates that the two vectors have the same slope or gradient, and will never intersect each other.

2. How can you determine if two vectors are parallel?

To determine if two vectors are parallel, you can use the dot product or cross product. If the dot product of two vectors is equal to zero, then they are parallel. Alternatively, if the cross product of two vectors is equal to zero, then they are also parallel.

3. Can two vectors be parallel if they have different magnitudes?

Yes, two vectors can be parallel even if they have different magnitudes. As long as they have the same direction, they will be considered parallel. However, if two vectors have different magnitudes and opposite directions, they will be considered anti-parallel.

4. What is the difference between parallel and anti-parallel vectors?

Parallel vectors have the same direction, while anti-parallel vectors have opposite directions. This means that parallel vectors have the same slope or gradient, while anti-parallel vectors have opposite slopes or gradients.

5. Can more than two vectors be parallel?

Yes, more than two vectors can be parallel. In fact, any number of vectors can be parallel as long as they have the same direction. However, it is not possible for more than two vectors to be anti-parallel.

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