n the product F = qv · B , take q = 4,
= 2.0i + 4.0j + 6.0k and = 136i -176j + 72k.
What then is in unit-vector notation if Bx = By?
~~may i get some assistance in this problem? so far.. i tried this..
136i-176j+72k = 4(2.0i+4.0j+6.0k)(B)
136i-176j+72k = (8i+16j+24k)(B)
[(136i-176j+72k)/(8i+16j+24k)] = B
17i-11j+3k = B
thats wrong.. so should i be doing this?
136i-176j+72k = (8xi+16yj+24zk)(Bxi+Byj+Bzk)
136i-176j+72k = (8xBxi+16yByj+24zBzk)
???
i need some help asap, that would be great. thanks again!
For Further Reading
* physics multiplying vectors - drwls, Thursday, March 29, 2007 at 4:37pm
Fill in the blanks in your question
<< In the product F = qv · B , take q = 4,
___= 2.0i + 4.0j + 6.0k and ___= 136i -176j + 72k.
What then is ___ in unit-vector notation if Bx = By>>
If the B vector is 2.0i + 4.0j + 6.0k, then Bx and By are NOT equal. Your question is incomplete and does not make sense.
* physics multiplying vectors - bobpursley, Thursday, March 29, 2007 at 4:38pm
You didn't multiply...
136i-176j+72k = (8i+16j+24k)(B)
But B= Bxi +Byj + Bzk
136i-176j+72k = (8i+16j+24k)(Bxi +Byj + Bzk)
136i-176j+72k= 8Bx k -8By j + 16Bx k +16Bz i + 24Bx j- 24By i
Now gather the terms, set the i terms equal to i, and so on. Check my work, I did it in my head.
* physics multiplying vectors - sam, Thursday, March 29, 2007 at 9:37pm
sorry, the complete question is:
n the product F = qv · B , take q = 4,
v = 2.0i + 4.0j + 6.0k and F= 136i -176j + 72k.
What then is in unit-vector notation if Bx = By?
I still can't get the right answer though...
Bobpursley...at this step:
136i-176j+72k = (8i+16j+24k)x(Bxi+Byj+bzk) I didn't think that you could just multiply the two vectors on the right hand side since they are both vectors not scalars. I have 3 vectors and I am trying to solve for B. How do I do that after this step?
thanks, i figured it out.
To solve for B in the equation F = qv · B, where q = 4, v = 2.0i + 4.0j + 6.0k, and F = 136i - 176j + 72k, and given that Bx = By, let's go through the steps again.
Step 1: Express F in terms of B:
F = qv · B
F = 4(2.0i + 4.0j + 6.0k) · B
F = 8i + 16j + 24k · Bx + 16i + 32j + 48k · By + 24i + 48j + 72k · Bz
F = (8Bx + 16By + 24Bz)i + (16Bx + 32By + 48Bz)j + (24Bx + 48By + 72Bz)k
Note: We can assume Bx = By = k for simplicity, as stated in the question.
Step 2: Equate the corresponding components of F and express B in unit-vector notation:
8Bx + 16By + 24Bz = 136i - 176j + 72k
From the given assumption, Bx = By = k:
8k + 16k + 24Bz = 136i - 176j + 72k
40k + 24Bz = 136i - 176j + 72k
Equate the i, j, and k components separately:
40 = 136
0 = -176
8Bz = 72
Step 3: Solve for Bz:
From the equations, we find:
Bz = 9
Step 4: Substitute the value of Bz into the equation to find B:
40k + 24Bz = 136i - 176j + 72k
40k + 24(9) = 136i - 176j + 72k
40k + 216 = 136i - 176j + 72k
Equate the i, j, and k components separately:
40 = 136
0 = -176
40k + 216 = 72k
From the last equation, solve for k:
40k + 216 = 72k
216 = 32k
k = 6.75
Step 5: Express B in unit-vector notation:
Now that we have the value of k, we can express B in unit-vector notation.
B = Bx i + By j + Bz k
B = ki + kj + (6.75)k
B = (0i + 0j + 6.75k) = 6.75k
Therefore, B in unit-vector notation is 6.75k.