Physics 221 Calc-based question for homework

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1. Jan 20, 2017

AidenPhysica

1. The problem statement, all variables and given/known data
If vector d1--> is equal to 2i^-4j^+9k^ and vector d2-> is equal to 8i^-10j^+9k^, what is (d1-->+d2-->) * (d1--> X 4d2->)?

2. Relevant equations

3. The attempt at a solution
So I added up first two vectors and then multiplied it by the cross product but I get a vector and when I find its length its like 1931. I just want to know if this is even close.

2. Jan 20, 2017

Staff: Mentor

Hi AidenPhysica, Welcome to Physics Forums.

Your result does not look correct to me. Can you show the details of your calculations?

3. Jan 20, 2017

Staff: Mentor

$$(\vec{d_1} + \vec{d_2}) \cdot (\vec{d_1} \times 4 \vec{d_2})$$
?

If that is correct, then your result is wrong. What to you get when you take the cross product of two vectors?

4. Jan 20, 2017

AidenPhysica

Its right what you put except there has to be a 4 right in front of d2 so its multiplied by four.

5. Jan 20, 2017

Staff: Mentor

I've corrected it. So, what do you get when you take the cross product of two vectors?

6. Jan 20, 2017

AidenPhysica

Ok, so this is what I did. I first added up the two vectors to get 10i+-14j+18k. Then you do the cross product, so I did that operation of the cross product, which is basically how much two vectors are perpendicular to each other? So here is the matrix i j k on top second row is 2, -4, 9. Third row is 32i-40j+36k. The cross product of this matrix is

7. Jan 20, 2017

AidenPhysica

216i +216j+48k

8. Jan 20, 2017

Staff: Mentor

I'll give you a hint: the actual values of the vectors are not important.

What is the orientation of that vector with respect to the original vectors?

9. Jan 20, 2017

AidenPhysica

Then what I did was I multiplied each respective component of the first answer times the second to get 3815 after doing pythagrean theorem is that better?

10. Jan 20, 2017

AidenPhysica

OK, so what do you mean by orientation?

11. Jan 20, 2017

Staff: Mentor

Stop a minute. I want you to think about the problem first. You can calculate numerical values later.

The direction in which it points. When you take the cross product of two vectors, the resulting vector points in a very specific direction with respect to the two other vectors.

12. Jan 20, 2017

AidenPhysica

so isn't the cross product equal to magnitude of a times magnitude of b multiplied by sin of theta?

13. Jan 20, 2017

AidenPhysica

Isn't cross product equal to magnitude of a times magnitude of b times sin of theta?

14. Jan 20, 2017

AidenPhysica

so isn't it just: ok so we have 10.05 times 26.83 times sin of theta=309.22. So then theta=309.22/269.6*(arcsin)

15. Jan 20, 2017

AidenPhysica

I don't know it doesn't work.

16. Jan 20, 2017

AidenPhysica

I try plugging it into a times b sin theta = magnitude of cross product but it just doesn't work.

17. Jan 20, 2017

Staff: Mentor

18. Jan 20, 2017

AidenPhysica

so how do i find orientation though?

19. Jan 20, 2017

AidenPhysica

Is it in degrees? I am just confused I see the picture, its like perpendicular.

20. Jan 20, 2017

Staff: Mentor

Yes, the resulting vector is perpendicular to the plane of the two initial vectors.