The resultant of two forces P N and 3 N is a force of 7 N. If the direction of the 3 N force were reversed, the resultant would be $square root of 19$ N. The value of P is

5N

6N

4N

3N

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Solution

7² = P² + 3² + 2 × 3 × P cosθ …(1)

left parenthesis square root of 19 right parenthesis squared space equals space straight P squared space plus space left parenthesis negative 3 right parenthesis squared space plus 2 space straight x space left parenthesis negative 3 right parenthesis straight x space straight P space cos space straight theta space..... space left parenthesis 2 right parenthesis

adding we get
68 = 2P² + 18 ⇒ P = 5.

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