To find the resultant of two vectors acting at an angle, we can use the law of cosines. Let’s denote the two vectors as \( \vec{A} \) and \( \vec{B} \), where \( A = 3 \) units and \( B = 4 \) units, and the angle \( \theta = 60^\circ \).
The magnitude of the resultant vector \( R \) can be calculated using the formula:
\[ R = \sqrt{A^2 + B^2 + 2AB \cos(\theta)} \]
Substituting the values we have:
- \( A = 3 \)
- \( B = 4 \)
- \( \theta = 60^\circ \)
- \( \cos(60^\circ) = 0.5 \)
Now plug these values into the formula:
\[ R = \sqrt{3^2 + 4^2 + 2 \cdot 3 \cdot 4 \cdot \cos(60^\circ)} \] \[ R = \sqrt{9 + 16 + 2 \cdot 3 \cdot 4 \cdot 0.5} \] \[ R = \sqrt{9 + 16 + 12} \] \[ R = \sqrt{37} \]
Thus, the magnitude of the resultant vector \( R \) is:
\[ R \approx 6.08 \text{ units} \]
So, the resultant of the two vectors is approximately 6.08 units.
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