In 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...
I am stuck here:
136i-176j+72k=(8i+16j+24k)x(Bxi+Byj+bzk)
How do I solve for Bxi + Byj + Bzk???
Everything that I have tried is incorrect. Please help. thanks.
that should be F=qv x B. not dot product.
thanks, i figured it out.
To solve for Bxi + Byj + Bzk, you can use the cross product formula:
F = qv x B
Substituting the given values:
136i - 176j + 72k = (4)(2.0i + 4.0j + 6.0k) x (Bxi + Byj + Bzk)
Expanding the cross product on the right side:
136i - 176j + 72k = (8i + 16j + 24k)(Bzk) - (12i - 24j + 8k)(Byj) + (6i - 4j - 2k)(Bxi)
Comparing the coefficients:
136i - 176j + 72k = 8Bzk - 12Byj + 6Bxi
Now, equating the i, j, and k components separately:
136 = 6Bx
-176 = -12By
72 = 8Bz
Solving each equation:
Bx = 22.67
By = 14.67
Bz = 9
Now, to express B as a unit vector, you divide each component by the magnitude of B:
B = Bx i + By j + Bz k
= (22.67 / sqrt(22.67^2 + 14.67^2 + 9^2)) i + (14.67 / sqrt(22.67^2 + 14.67^2 + 9^2)) j + (9 / sqrt(22.67^2 + 14.67^2 + 9^2)) k
After calculating the denominator, you can simplify the expression to obtain the unit vector notation of B.