What is the scalar triple product of vectors a = (1, 2, 3), b = (4, 5, 6), c = (7, 8, 9)?

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Q: What is the scalar triple product of vectors a = (1, 2, 3), b = (4, 5, 6), c = (7, 8, 9)?

Solution: Scalar triple product = a · (b × c). Since b and c are linearly dependent, b × c = 0, hence the scalar triple product is 0.

Steps: 8

Step 1: Identify the vectors a, b, and c. Here, a = (1, 2, 3), b = (4, 5, 6), and c = (7, 8, 9).
Step 2: Understand that the scalar triple product is calculated as a · (b × c).
Step 3: Calculate the cross product b × c. This involves finding a vector that is perpendicular to both b and c.
Step 4: Check if vectors b and c are linearly dependent. If they are, it means they lie on the same line, and their cross product will be zero.
Step 5: Since b and c are linearly dependent, we find that b × c = 0.
Step 6: Substitute the result of the cross product back into the scalar triple product formula: a · (b × c) = a · 0.
Step 7: Calculate the dot product of a and 0, which is always 0.
Step 8: Conclude that the scalar triple product of the given vectors is 0.