# More vectors

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• Sep 30th 2012, 09:49 PM
Oldspice1212
More vectors
Given two vectors Vector A = 4.00i+7.00j and Vector B = 5.00i-2.00j , find the vector product A*B (expressed in unit vectors).

I got 20.0i+14.0j+0k

What is magnitude of the vector product?

Either 280 or 0

• Sep 30th 2012, 09:54 PM
chiro
Re: More vectors
Hey Oldspice1212.

Please state the problem precisely: I have absolutely no idea what you are trying to actually calculate since you just give an answer without a question.
• Sep 30th 2012, 09:58 PM
Oldspice1212
Re: More vectors
Well the first one it asked for Vectors A*B =which I have to put it in terms of unit vectors and second one is asking the same thing but now it's an absolute value so |A*B| for the magnitude
• Sep 30th 2012, 10:04 PM
chiro
Re: More vectors
Yeah but what is A and what is B?
• Sep 30th 2012, 10:13 PM
Oldspice1212
Re: More vectors
Oh I'm sorry I thought it was showing on my thread, I'll fix it right now

There we go, let me know if it makes sense now.
• Oct 1st 2012, 04:50 AM
TwoPlusTwo
Re: More vectors
Quote:

Originally Posted by Oldspice1212
Given two vectors Vector A = 4.00i+7.00j and Vector B = 5.00i-2.00j , find the vector product A*B (expressed in unit vectors).

I got 20.0i+14.0j+0k

What is magnitude of the vector product?

Either 280 or 0

It looks like you have been trying to take the dot product, not the vector product, or cross product.

The dot product results in a scalar, not a vector:

A dot B = 4*5 + 7*(-2) = 20 - 14 = 6

What method have you learned for calculating the cross product? Keep in mind the answer should be a vector that's perpendicular to both A and B.
• Oct 1st 2012, 11:06 AM
Oldspice1212
Re: More vectors
Ah I have no clue what the vector product is lol, I always thought you're suppose to use dot product for those kind of questions. What's the vector product?
• Oct 1st 2012, 11:18 AM
Plato
Re: More vectors
Quote:

Originally Posted by Oldspice1212
Ah I have no clue what the vector product is lol, I always thought you're suppose to use dot product for those kind of questions. What's the vector product?

The dot product is a scalar, a number, $\vec{a}\cdot\vec{b}$ .

The cross product, vctor product is a vector, $\vec{a}\times\vec{b}$.
• Oct 1st 2012, 11:41 AM
Oldspice1212
Re: More vectors
Didn't I do that? The answer should be the same since you're multiplying both right?
• Oct 1st 2012, 12:01 PM
Plato
Re: More vectors
Quote:

Originally Posted by Oldspice1212
Didn't I do that? The answer should be the same since you're multiplying both right?

There is no such an operation as vector multiplication.

There are dot products and cross products but no vector multiplication.
• Oct 1st 2012, 12:14 PM
Oldspice1212
Re: More vectors
Ok so now I got 0i+0j - 43z...
• Oct 1st 2012, 02:45 PM
Oldspice1212
Re: More vectors
Is this correct since there are no z components not sure if it should be treated as 1 or 0
• Oct 1st 2012, 02:57 PM
Plato
Re: More vectors
Quote:

Originally Posted by Oldspice1212
Is this correct since there are no z components not sure if it should be treated as 1 or 0

If $A=4i+7j~\&~B=5i-2j$ then $A\times B=-43k$
• Oct 1st 2012, 04:39 PM
Oldspice1212
Re: More vectors
Quote:

Originally Posted by Plato
If $A=4i+7j~\&~B=5i-2j$ then $A\times B=-43k$

Yes I understand that but I don't get the i and j should they be 0 or should I have put the z components as 1?
• Oct 1st 2012, 06:54 PM
Prove It
Re: More vectors
Quote:

Originally Posted by Plato
There is no such an operation as vector multiplication.

There are dot products and cross products but no vector multiplication.

Actually Plato, the dot product is often called the scalar product, while the cross product is often called the vector product...

Anyway, the easiest way to evaluate a vector product is using a determinant. If you have two vectors \displaystyle \begin{align*} A = a_i \mathbf{i} + a_j\mathbf{j} + a_k \mathbf{k} \end{align*} and \displaystyle \begin{align*} B = b_i\mathbf{i} + b_j\mathbf{j} + b_k\mathbf{k}\end{align*}, then their vector product is

\displaystyle \begin{align*} A \times B = \left| \begin{matrix} i & j & k \\ a_i & a_j & a_k \\ b_i & b_j & b_k \end{matrix} \right| \end{align*}
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