**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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Can you please do all of them. thank you
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wo vectors are defined in component form below. Use them to perform the following exercises. Note: £, §, and 2 are unit vectors of the Cartesian coordinate system defined by £ × 9 = z. S = - D Č = -152 + 82 D = -42 – 39 T = Č XD F = 5 le| = 17 Determine S. Show your ster Determine T. (Your answer should be an expression in component form.) Show your steps Determine the smallest angle between D and ý when they are drawn tail-to-tail.
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