suppose a force given as F_1 = 24 N and F_2 = 50 N act through points AB and AC where OA = 2i +3j , OB = 5i + 6j and OC = 7i + 8j (a) find in vector notation F_1 and F


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Question Number 98208 by Rio Michael last updated on 12/Jun/20

$suppose a force given as F_{1} = 24 N and F_{2} = 50 N act through$ $points A B and A C where O A = 2 i + 3 j, O B = 5 i + 6 j and$ $O C = 7 i + 8 j$ $(a) find in vector notation F_{1} and F_{2}$ $then find thier resultant .$
Commented by mr W last updated on 12/Jun/20

$A B = O B - O A = 3 i + 3 j$ $F_{1} =∣ F_{1} ∣ \times \frac{A B}{∣ A B ∣} = 12 \sqrt{2} (i + j)$ $A C = O C - O A = 5 i + 5 j$ $F_{2} =∣ F_{2} ∣ \times \frac{A B}{∣ A B ∣} = 25 \sqrt{2} (i + j)$ $F_{1} + F_{2} = (12 + 25) \sqrt{2} (i + j) = 37 \sqrt{2} (i + j)$ $∣ F_{1} + F_{2} ∣= 37 \sqrt{2} \sqrt{1^{2} + 1^{2}} = 74 K N$
Commented by Rio Michael last updated on 12/Jun/20

$thanks for that$
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