If B is added to C = 6.5i + 4.6j, the result is a vector in the positive direction of the y axis, with a magnitude equal to that of C. What is the magnitude of B?

0 if you add 0 to c you get the same vector.

To solve this problem, we need to find the magnitude of the vector B.

We are given that when B is added to C, the resultant vector is in the positive direction of the y-axis and has the same magnitude as C.

Let's first find the magnitude of vector C.

The magnitude of a vector is calculated using the formula:
Magnitude = sqrt(x^2 + y^2)

In this case, the vector C is given as 6.5i + 4.6j, where i and j are unit vectors in the x and y directions, respectively.

So, the x-component of C is 6.5 and the y-component is 4.6.

Now, we can calculate the magnitude of C as:
Magnitude of C = sqrt((6.5)^2 + (4.6)^2)

Next, we know that when B is added to C, the resultant vector has the same magnitude as C and is in the positive direction of the y-axis.

Since the resultant vector is in the positive direction of the y-axis, the x-component of the resultant vector must be zero.

Therefore, the x-component of vector B must be the negative of the x-component of vector C, which is -6.5.

So, the vector B can be written as -6.5i + Bj, where B is the magnitude of vector B.

Now, the magnitude of the resultant vector (B + C) is equal to the magnitude of C.

Using the formula for magnitude as mentioned earlier, we can equate the magnitudes of B + C and C:

Magnitude of B + C = Magnitude of C

Now, let's substitute the values:

Magnitude of (-6.5i + Bj + 6.5i + 4.6j) = Magnitude of (6.5i + 4.6j)

Simplifying the equation:

Magnitude of (Bj + 4.6j) = Magnitude of (6.5i + 4.6j)

(Notice that the i terms cancel out because the x-components are equal in magnitude but opposite in sign)

Magnitude of (B + 4.6) = Magnitude of 4.6

(B + 4.6) = 4.6 (taking the magnitudes on both sides)

B = 0

Therefore, the magnitude of vector B is 0.