# Cross product and dot product scalars

1. Feb 12, 2008

### TS656577

1. The problem statement, all variables and given/known data
If d1 = 4i - 10j + 2k and d2 = 9i - 10j + 6k, then what is (d1 + d2) · (d1 × 4d2)?

2. Relevant equations
Know how to do the cross product and dot product

3. The attempt at a solution
For the answer i got 9.6i + 56j -127.68k. How do i express that as a scalar for an online program that only has one box to type in?

2. Feb 12, 2008

### Kurdt

Staff Emeritus

3. Feb 12, 2008

### TS656577

I didnt think my answer was wrong though?

4. Feb 12, 2008

### Kurdt

Staff Emeritus
If you take the dot product of two vectors then the answer will be a scalar not a vector. If you post what you've done it'll be easier to identify where you went wrong.

5. Feb 12, 2008

### TS656577

First i calculated the quantity of d1+d2 and got 13i + 0j +8k. Then i went to the other side of the problem and distributed the 4 to the d2 terms and got a result of 36i - 40j + 24k. After that, i took the cross product of d1 and 4d2 and got -160i -24j - 200k. Then i took the dot product and got -2080i - 1600k (sorry i posted the wrong answer the first time, my bad)

6. Feb 12, 2008

### Kurdt

Staff Emeritus
For the addition of d1 and d2, -10 +(-10) does not equal 0.

For the cross product, that should be +200k.

The dot product of two vectors is:

$$\mathbf{a}\cdot \mathbf{b} = a_x b_x + a_y b_y + a_z b_z$$

Last edited: Feb 12, 2008
7. Feb 12, 2008

### TS656577

so then when i add that up, it equals one number? for example if i had axbx=3, ayby=4 and azbz=2, then i would have something that resembles 3+4+2 and would i use 9 for the answer?

8. Feb 12, 2008

### ||spoon||

yes, thats correct.

9. Feb 12, 2008

### TS656577

i got -3200 for my final answer, but that seems wrong..

10. Feb 12, 2008

### Kurdt

Staff Emeritus
Again if you post exactly what you've done when computing the dot product it will be easier to advise you where you went wrong.

11. Feb 12, 2008

### TS656577

after doing the cross product for d1xd2, i got -160i -24j -200k. After that, i multiplied by the sum i got for the d1+d2 section. So in the end, i multiplied -160 times 13, -24 times -20, and -200 times 8. Then i had -2080 + 480 - 1600

12. Feb 12, 2008

### Kurdt

Staff Emeritus
If you look in my previous post I said that after the cross product you should have +200k not -200k.

13. Feb 12, 2008

### Marco_84

remeber that the cross product is something like;

[-,-]: VxV----->V; \\ V=vector space

so gives you back another vector;

while the dot product (generally an inner product) is something like;

(-,-): VxV------>C \\ C=complex field

know how to make both in an euclidean orthonormal basis and you'll get your answer;

regards;
marco;

14. Feb 12, 2008

### TS656577

got it, thanks guys...sorry for bein dumb (sick last few days)