Question

In the construction of a bridge, the support cables form specific angles to each other. The angle between two vectors representing the tensile force in two cables can influence the load distribution of the structure. Data: U=(3,4,0) V=(1,2,2) The scalar product is used to calculate the cosine of the angle θ between two vectors, according to the formula: Where: Alternatives for question 2 43°, cos(43°)=0.731 60°, cos?(60°)=0.5 45°, cos?(45°)=0.707 30°, cos?(30°)=0.866

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Answer to a math question In the construction of a bridge, the support cables form specific angles to each other. The angle between two vectors representing the tensile force in two cables can influence the load distribution of the structure. Data: U=(3,4,0) V=(1,2,2) The scalar product is used to calculate the cosine of the angle θ between two vectors, according to the formula: Where: Alternatives for question 2 43°, cos(43°)=0.731 60°, cos?(60°)=0.5 45°, cos?(45°)=0.707 30°, cos?(30°)=0.866

$Expert avatar$

Hermann

4.6

126 Answers

\begin{align*}\cos(\theta) &= \frac{U \cdot V}{||U|| \cdot ||V||} \\U \cdot V &= 3 \cdot 1 + 4 \cdot 2 + 0 \cdot 2 = 3 + 8 + 0 = 11 \\||U|| &= \sqrt{3^2 + 4^2 + 0^2} = \sqrt{9 + 16 + 0} = \sqrt{25} = 5 \\||V|| &= \sqrt{1^2 + 2^2 + 2^2} = \sqrt{1 + 4 + 4} = \sqrt{9} = 3 \\\cos(\theta) &= \frac{11}{5 \cdot 3} = \frac{11}{15} \approx 0,733\end{align*}

\leftarrow \text{The closest given value to } 0.733 \text{ is } \cos(43^\circ) \text{, while the correct answer's angle should be } \theta = 45^\circ.

\boxed{45^\circ}

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