If A 280i Bz 0 B 9886 and A times B 3640K determine the

If A = 2.80i, B_z = 0, |B| = 9.886, and A times B = 3.640K, determine the x component of B. (Assume the x-component is positive.)_______

Solution

A = 2.80 i

Let\'s assume

B = Bx i + By j + Bz k

Bz = 0

Now,

B = Bx i + By j

|B| = 9.886 = sqrt (Bx^2 + By^2)

Bx^2 + By^2 = 9.886^2

AxB = 3.640 k

AxB = (2.80 i)x(Bx i + By j) = 3.640 k

since, ixi = 0 and ixj = k

AxB = 2.8*By k = 3.640 k

By = 3.640/2.8 = 1.3 j

Bx^2 + By^2 = 9.886^2

Bx^2 + 1.3^2 = 9.886^2

Bx = sqrt (9.886^2 - 1.3^2)

Bx = 9.800 i

X-component of B = 9.800