Two vectors acting through a point are in the ratio `3 : 5`. If the angle between them is `60^(@)` and the magnitude of their resultant is `35` , find the magnitude of vectors.

Explanation

To solve the problem step by step, we will follow the given information and apply the relevant formulas.

### Step 1: Define the Vectors
Let the magnitudes of the two vectors be \( A \) and \( B \). According to the problem, the ratio of the magnitudes of the vectors is given as \( 3:5 \). We can express this as:
\[ A = 3x \quad \text{and} \quad B = 5x \]
where \( x \) is a common factor.
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