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?
~~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!
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.
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.
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...
If Bx = By, then B = Bxi + Byj + Bzk = Byi + Byj + Bzk = By(i + j + k).
Now, substitute this into the equation F = qv · B:
F = 4(2.0i + 4.0j + 6.0k) · By(i + j + k)
= 8Byi + 16Byj + 24Byk
Now, set this equal to the given F:
136i - 176j + 72k = 8Byi + 16Byj + 24Byk
Solve for By:
By = (136i - 176j + 72k) / (8i + 16j + 24k)
By = 17i - 11j + 3k
Therefore, in unit-vector notation, B = 17i - 11j + 3k.
No problem! Let's go through the problem step by step to find the right answer.
Given:
q = 4
v = 2.0i + 4.0j + 6.0k
F = 136i - 176j + 72k
Bx = By (let's say they are both equal to B)
The formula for the product F = qv · B is:
F = q(v · B)
To find B, we can rearrange the formula as follows:
B = (1/q)(F / v)
Substituting the given values:
B = (1/4)(136i - 176j + 72k) / (2.0i + 4.0j + 6.0k)
To divide a vector by a vector, we can use the dot product formula:
A · B = AxBx + AyBy + AzBz
Applying the dot product formula:
B = (1/4)(136i - 176j + 72k) / (2.0i + 4.0j + 6.0k)
= (1/4)((136 * 2.0) - (176 * 4.0) + (72 * 6.0)) / ((2.0 * 2.0) + (4.0 * 4.0) + (6.0 * 6.0)) * B
Now, simplify the equation:
B = (1/4)(272 - 704 + 432) / (4 + 16 + 36) * B
= (1/4)(0) / (56) * B
= 0 * B
= 0
Therefore, if Bx = By, then B = 0 in unit-vector notation.
In order to solve for B in unit vector notation, we can use the equation F = qv · B and substitute the given values.
Given: q = 4, v = 2.0i + 4.0j + 6.0k, F = 136i - 176j + 72k, and Bx = By
Let's substitute the values into the equation and solve step-by-step:
F = qv · B
136i - 176j + 72k = 4(2.0i + 4.0j + 6.0k) · B
Distribute the 4 through the vector in the parentheses on the right side:
136i - 176j + 72k = (8i + 16j + 24k) · B
Now, let's expand the dot product by multiplying the corresponding components:
136i - 176j + 72k = 8iB + 16jB + 24kB
Since Bx = By, we can say B = Bxi + Bxi + Bzk, so let's substitute B into the equation:
136i - 176j + 72k = 8i(Bxi) + 16j(Byj) + 24k(Bzk)
Now, let's gather the terms with the same unit vectors:
136i - 176j + 72k = (8Bx)i + (16By)j + (24Bz)k
Since the coefficient of i on the left side is equal to the coefficient of i on the right side, we can equate them:
136i = (8Bx)i
By equating the coefficients, we get:
136 = 8Bx
Solving for Bx:
Bx = 136/8 = 17
Similarly, we can equate the coefficients of Bj and Bk:
-176 = 16By
Solving for By:
By = -176/16 = -11
And:
72 = 24Bz
Solving for Bz:
Bz = 72/24 = 3
Therefore, in unit vector notation, B = 17i - 11j + 3k.