IF Vector B added to vector c=3x+4y,the result is in +ve y_axis with magnitude equal to that c,what is the magnitude of B?
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To determine the magnitude of vector B, we first need to find the magnitude of vector C.
Let's break down the problem step by step:
1. Start with vector C: C = 3x + 4y.
2. We are told that when vector B is added to vector C, the resulting vector is in the positive y-axis direction with a magnitude equal to that of vector C.
So, if we add vector B to vector C, the resulting vector points in the positive y-axis direction and has the same magnitude as vector C.
3. Since vector C is given by C = 3x + 4y, its magnitude can be calculated using the Pythagorean theorem:
Magnitude of C = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.
So, the magnitude of vector C is 5.
4. Now, we need to find the magnitude of vector B.
Since the resulting vector (C + B) has a magnitude of 5 and points in the positive y-axis direction, we can write it as B = 0x + 5y.
Comparing this to the given expression for vector C (3x + 4y), we can see that the y-component of vector B is 5.
5. To find the magnitude of vector B, we can calculate it directly as the magnitude of B = √(0^2 + 5^2) = √25 = 5.
Therefore, the magnitude of vector B is also 5.