Finding Components of Cross Product for Vectors A and B

[angel120]

Homework Statement

Vector A = 3.5i + 1.8j and vector B = 1.7i + 4.8j . Find the components of A x B:

Homework Equations

AxB = AB sin(theta)

The Attempt at a Solution

Since vector A=3.5i+1.8j and B=1.7i+4.8j, I translated that into vectors. So, A is 3.94 @ 27.77*, and B is 5.09 @ 70.56*. This means that the angle between A and B is 42.79*.

Using the AxB formula, I have 13.62. However, the problem (it's on WebAssign) wants the i, j, and k components.

I tried the AxB formula with the individual i and j components, and I got 4.04 for the i direction, and 5.87 for the j direction. However, they're both wrong, and I have no idea how to find out the k direction...

Help!

Thanks in advance,
-Angel.

 

[cse63146]

k is the third dimesion (or 3rd component in this case). A and B are 2 dimensions.

 

[angel120]

I understand that the i, j, and k components are the x, y, and z directions, respectively. My frustration is that I believe I'm following the correct formula, but I still get the wrong answer. Where is my reasoning flawed?

I have tried the following:
AxB = (3.94)(5.09)sin(42.79) = 13.62, however, WebAssign wants the answer in components.
So, I tried this:
AxB = (3.5i)(1.7i)sin(42.79) = 4.04i

and then
AxB = (1.8)(4.8)sin(42.79) = 5.87j

When I entered these two (out of three) answers, they were both marked wrong.

 

[borgwal]

The formula you try to use is for the magnitude of the vector axb, but the question asks for the vector itself.

Do you know the way to calculate a cross product as if it were a determinant?

axb=|i j k; a_i a_j a_k; b_i b_j b_k|

 

[Ithryndil]

When you cross two vectors the resultant vector will be orthogonal to both original vectors. Keep that in mind.

 

[nasu]

You can multiply by components, but:

i x i=0 (same for j x j)
i x j =k
j x i = -k

Try this.
Newer mind the sin. Multiply the two vectors as you'll do for two binomials.