What is the scalar triple product of vectors A = i + j + k, B = 2i + 3j + k, and

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Question: What is the scalar triple product of vectors A = i + j + k, B = 2i + 3j + k, and C = 3i + j + 2k?

Options:

Correct Answer: 0

Solution:

Scalar triple product = A · (B × C) = |i  j  k| |1  1  1| |2  3  1| |3  1  2| = 0.

What is the scalar triple product of vectors A = i + j + k, B = 2i + 3j + k, and C = 3i + j + 2k?

What is the scalar triple product of vectors A = i + j + k, B = 2i + 3j + k, and C = 3i + j + 2k?

Step 1: Identify the vectors A, B, and C. A = i + j + k, B = 2i + 3j + k, C = 3i + j + 2k.
Step 2: Write the vectors in component form. A = (1, 1, 1), B = (2, 3, 1), C = (3, 1, 2).
Step 3: Calculate the cross product B × C. Use the determinant of a 3x3 matrix with i, j, k in the first row, components of B in the second row, and components of C in the third row.
Step 4: Set up the determinant: | i j k | | 2 3 1 | | 3 1 2 |.
Step 5: Calculate the determinant to find B × C.
Step 6: Once you have B × C, calculate the dot product A · (B × C).
Step 7: The result of the dot product gives you the scalar triple product.
Step 8: In this case, the scalar triple product is 0.

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