Question

In the Cross(or vector) product F=qv x B we know that q=1

F=-28i +4j -16k

v=-4i +4j +8k

B=Bxi +Byj + Bzk

what then is B in unit-vector notation if Bx=By?

B= [ ]i + [ ]j +[ ]k

Answer 1

To find the vector B given Bx = By, and knowing the charge q, velocity v, and force F, one applies the cross product formula and the properties of cross multiplication of unit vectors.

Step-by-step explanation:

Understanding the cross product is essential in physics, especially when dealing with magnetic forces. The question is about finding vector B when Bx = By, and we already know that for the cross product of unit vectors i, j, and k, the result is mutually orthogonal vectors such that i x j = k, j x k = i, and k x i = j. Given that F, q, and v are provided, and knowing that F = qv x B, we can apply the definition of the cross product along with the properties of the unit vectors to find the components of B.

Since we know that Bx = By and we're given F and v, we apply

F = qv x B

and the formula for the cross product of vectors:

C = A x B = (Ay Bz - Az By)i + (Az Bx - Ax Bz)j + (Ax By - Ay Bx)k

to find the missing components of B in unit-vector notation.