# Two vectors are parallel if their cross product is 0?

• teffy3001
In summary: There's no 'b' in your problem statement. What is it?Dick, the b is in the v component. I missed it at first glance too.Anyway teffy, what conditions do you know that tests if two vectors are parallel?v=5i + bjthats where the b is..Ooops. Missed it. So u-v=4i+(-6-b)j. Now answer arunbg's question.um that two vectors are parallel if their cross product is 0?...So what do you get when you take the cross product?i think that's where my problem lies now...im not sure
teffy3001
the question is:

u = 9i-6j
and
v = 5i+bj

for what value of b would u-v point in the same direction as w = 7i-3j?

can anyone help me get started on this problem, I am not looking for answers just a little bit of help because I'm confused.. thanks

There's no 'b' in your problem statement. What is it?

Dick, the b is in the v component. I missed it at first glance too.
Anyway teffy, what conditions do you know that tests if two vectors are parallel?

v=5i + bj

thats where the b is..

Ooops. Missed it. So u-v=4i+(-6-b)j. Now answer arunbg's question.

um that two vectors are parallel if their cross product is 0?...

So what do you get when you take the cross product?

i think that's where my problem lies now...im not sure how to find that out.

That's one way. But in only really works in three dimensions. More generally vectors A and B point in the same direction if A=k*B for some k>0 (any nonzero k if you don't mind them pointing in opposite directions). So you could set the ratio of the components equal.

okay so then how do i find the value of b?

Write down expressions for the ratio of the i components and the ratio of the j components and set them equal.

Pictures often help with vectors!

(Cross-product will work, but, as you've found out, it's not particularly easy:yuck:, and there is a simpler way)

If you're stuck, it often helps to draw a picture.

You did head this as a vectors problem, rather than an algebra one.

So draw (only roughly) the two vectors you have to make parallel!

What trigonometric thing could you measue to check if they're parallel?

## 1. What is a cross product?

A cross product is a mathematical operation that takes two vectors as input and produces a vector as output. It is also known as a vector product or a vector cross product.

## 2. How is the cross product calculated?

The cross product of two vectors, A and B, is calculated by taking the magnitude of the two vectors, multiplying them, and then multiplying by the sine of the angle between them. The resulting vector is perpendicular to both A and B.

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

Two vectors are parallel if they have the same direction or are pointing in exactly opposite directions. This means that their cross product is equal to 0.

## 4. Why is the cross product used to determine if two vectors are parallel?

The cross product is used because it gives us information about the direction and perpendicularity of two vectors. If the cross product of two vectors is equal to 0, then we know that the vectors are either parallel or antiparallel (pointing in opposite directions).

## 5. Can two non-parallel vectors have a cross product of 0?

No, two non-parallel vectors cannot have a cross product of 0. The only way for the cross product to be 0 is if the vectors are parallel or antiparallel.

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