Explanation Given: The figure is: Let the vertices of the tetrahedron is ( 1 , 0 , 0 ) , ( 0 , 1 , 0 ) , ( 0 , 0 , 1 ) and ( 1 , 1 , 1 ) . Also, the centroid is ( 1 2 , 1 2 , 1 2 ) Formula used: The dot product of v and w is v ⋅ w = ‖ v ‖ ‖ w ‖ cos θ . Calculation: Let the vertices of the tetrahedron is ( 1 , 0 , 0 ) , ( 0 , 1 , 0 ) , ( 0 , 0 , 1 ) and ( 1 , 1 , 1 ) . Also, the centroid is ( 1 2 , 1 2 , 1 2 ) . Find the angle between two of the bond. Write the bond as a vector. Take the vector from the center whose tail is at the carbon atom and head is at each of the hydrogen atom. Take the hydrogen atoms ( 1 , 0 , 0 ) and ( 0 , 1 , 0 ) . Now, the two vectors are: a 1 = 〈 1 , 0 , 0 〉 − 〈 1 2 , 1 2 , 1 2 〉 = 〈 1 2 , − 1 2 , − 1 2 〉 a 1 = 〈 0 , 1 , 0 〉 − 〈 1 2 , 1 2 , 1 2 〉 = 〈 − 1 2 , 1 2 , − 1 2 〉 Find the value of | a 1 | and | a 2 | ...

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Author: Rogawski

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Chapter 13.3, Problem 81E

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Use the dot product to find the bond angle $α$ formed between any two of the line segments.

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Chapter 13.3, Problem 80E

Chapter 13.3, Problem 82E

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Use the dot product to find the bond angle α formed between any two of the line segments.

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Use the dot product to find the bond angle $α$ formed between any two of the line segments.

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