Textbook Question
For the two vectors A and B in Fig. E1.39, find the scalar product A · B
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3. Vectors
Calculating Dot Product Using Components
Multiple Choice
Calculate the dot product between A = (6.6 i - 3.4 j - 6.4 k ) and B = (8.6 i + 2.6 j - 5.8 k).
A
85
B
15 i - 0.80 j - 12 k
C
11
D
57 i - 8.8 j + 37 k
1 Comment
Verified step by step guidance1
Understand the concept of the dot product: The dot product of two vectors \( \mathbf{A} = a_1 \mathbf{i} + a_2 \mathbf{j} + a_3 \mathbf{k} \) and \( \mathbf{B} = b_1 \mathbf{i} + b_2 \mathbf{j} + b_3 \mathbf{k} \) is calculated as \( \mathbf{A} \cdot \mathbf{B} = a_1 b_1 + a_2 b_2 + a_3 b_3 \).
Identify the components of vector \( \mathbf{A} \): \( a_1 = 6.6 \), \( a_2 = -3.4 \), \( a_3 = -6.4 \).
Identify the components of vector \( \mathbf{B} \): \( b_1 = 8.6 \), \( b_2 = 2.6 \), \( b_3 = -5.8 \).
Substitute the components into the dot product formula: \( \mathbf{A} \cdot \mathbf{B} = (6.6)(8.6) + (-3.4)(2.6) + (-6.4)(-5.8) \).
Calculate each term separately: \( (6.6)(8.6) \), \( (-3.4)(2.6) \), and \( (-6.4)(-5.8) \), then sum these results to find the dot product.
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