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Use the information about vectors S and T provided below in the following exercises. T.x=0m |T|= 10m Tŷ = -3 m T.2=0 m |S| = 12.8m b) d) 0 5.x = 2m S.ŷ = 10 m 5.2 = -8 m Draw the direction of the missing Cartesian unit vector 2. Write the expression for the vector component of Š in the 2 direction. HW 14 Chosen coordinate System ↑ x Determine the smallest angle between S and 2, when they are drawn tail to tail. Express S and T in component form, using the chosen coordinate system. Determine S.T. ŷ 2

Use the information about vectors S and T provided below in the following exercises. T.x=0m |T|= 10m Tŷ = -3 m T.2=0 m |S| = 12.8m b) d) 0 5.x = 2m S.ŷ = 10 m 5.2 = -8 m Draw the direction of the missing Cartesian unit vector 2. Write the expression for the vector component of Š in the 2 direction. HW 14 Chosen coordinate System ↑ x Determine the smallest angle between S and 2, when they are drawn tail to tail. Express S and T in component form, using the chosen coordinate system. Determine S.T. ŷ 2

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**Educational Content for HW 14 on Vectors** **Instructions:** Use the information about vectors \( \vec{S} \) and \( \vec{T} \) provided below in the following exercises. --- **Vector Information:** - \( |\vec{S}| = 12.8 \, m \) - \( \vec{S} \cdot \hat{x} = 2 \, m \) - \( \vec{S} \cdot \hat{y} = 10 \, m \) - \( \vec{S} \cdot \hat{z} = -8 \, m \) - \( |\vec{T}| = 10 \, m \) - \( \vec{T} \cdot \hat{x} = 0 \, m \) - \( \vec{T} \cdot \hat{y} = -3 \, m \) - \( \vec{T} \cdot \hat{z} = 0 \, m \) --- **Chosen Coordinate System Diagram:** - The coordinate system shows three unit vectors: - \( \hat{x} \) is pointing upwards. - \( \hat{y} \) is represented by a circle with a dot in the center (indicating out of the page). - \( \hat{z} \) is pointing to the right. --- **Exercises:** a) *Draw the direction of the missing Cartesian unit vector \( \hat{z} \).* b) *Write the expression for the vector component of \( \vec{S} \) in the \( \hat{z} \) direction.* c) *Determine the smallest angle between \( \vec{S} \) and \( \hat{z} \), when they are drawn tail to tail.* d) *Express \( \vec{S} \) and \( \vec{T} \) in component form, using the chosen coordinate system.* e) *Determine \( \vec{S} \cdot \vec{T} \) (the dot product).*
Transcribed Image Text:**Educational Content for HW 14 on Vectors** **Instructions:** Use the information about vectors \( \vec{S} \) and \( \vec{T} \) provided below in the following exercises. --- **Vector Information:** - \( |\vec{S}| = 12.8 \, m \) - \( \vec{S} \cdot \hat{x} = 2 \, m \) - \( \vec{S} \cdot \hat{y} = 10 \, m \) - \( \vec{S} \cdot \hat{z} = -8 \, m \) - \( |\vec{T}| = 10 \, m \) - \( \vec{T} \cdot \hat{x} = 0 \, m \) - \( \vec{T} \cdot \hat{y} = -3 \, m \) - \( \vec{T} \cdot \hat{z} = 0 \, m \) --- **Chosen Coordinate System Diagram:** - The coordinate system shows three unit vectors: - \( \hat{x} \) is pointing upwards. - \( \hat{y} \) is represented by a circle with a dot in the center (indicating out of the page). - \( \hat{z} \) is pointing to the right. --- **Exercises:** a) *Draw the direction of the missing Cartesian unit vector \( \hat{z} \).* b) *Write the expression for the vector component of \( \vec{S} \) in the \( \hat{z} \) direction.* c) *Determine the smallest angle between \( \vec{S} \) and \( \hat{z} \), when they are drawn tail to tail.* d) *Express \( \vec{S} \) and \( \vec{T} \) in component form, using the chosen coordinate system.* e) *Determine \( \vec{S} \cdot \vec{T} \) (the dot product).*
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