Answer:
We can solve for the magnitude of vector C by first isolating it on one side of the equation:
2A - 6B + 3C = 2j
3C = 2j - 2A + 6B
C = (2/3)j - (2/3)A + 2B
Now that we have an expression for vector C, we can find its magnitude using the formula:
|C| = sqrt(Cx^2 + Cy^2 + Cz^2)
where Cx, Cy, and Cz are the x, y, and z components of vector C, respectively.
Since the equation only gives us information about the y-component of vector C, we can assume that the x and z components are zero. Therefore,
Cx = 0
Cy = 2/3
Cz = 0
|C| = sqrt((0)^2 + (2/3)^2 + (0)^2)
|C| = sqrt(4/9)
|C| = 2/3
Therefore, the magnitude of vector C is 2/3.