Cross product and dot product scalars

[TS656577]

Homework Statement

If d1 = 4i - 10j + 2k and d2 = 9i - 10j + 6k, then what is (d1 + d2) · (d1 × 4d2)?

Homework Equations

Know how to do the cross product and dot product

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?

 

[Kurdt]

Your answer should be a scalar anyway if you had to take the dot product (commonly known as the scalar product). I suggest you check your answer.

 

[TS656577]

I didnt think my answer was wrong though?

 

[Kurdt]

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.

 

[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)

 

[Kurdt]

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

 

[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?

 

[||spoon||]

yes, that's correct.

 

[TS656577]

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

 

[Kurdt]

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.

 

[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

 

[Kurdt]

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

 

[Marco_84]

Homework Statement

If d1 = 4i - 10j + 2k and d2 = 9i - 10j + 6k, then what is (d1 + d2) · (d1 × 4d2)?

Homework Equations

Know how to do the cross product and dot product

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?

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;

 

[TS656577]

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