If C = (3, -1, 2) and D = (4, 2, 1), calculate C · D.

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Question: If C = (3, -1, 2) and D = (4, 2, 1), calculate C · D.

Options:

Correct Answer: 11

Solution:

C · D = 3*4 + (-1)*2 + 2*1 = 12 - 2 + 2 = 12.

If C = (3, -1, 2) and D = (4, 2, 1), calculate C · D.

If C = (3, -1, 2) and D = (4, 2, 1), calculate C · D.

Step 1: Identify the components of vector C, which are (3, -1, 2).
Step 2: Identify the components of vector D, which are (4, 2, 1).
Step 3: Multiply the first component of C (3) by the first component of D (4). This gives 3 * 4 = 12.
Step 4: Multiply the second component of C (-1) by the second component of D (2). This gives -1 * 2 = -2.
Step 5: Multiply the third component of C (2) by the third component of D (1). This gives 2 * 1 = 2.
Step 6: Add the results from Steps 3, 4, and 5 together: 12 + (-2) + 2.
Step 7: Calculate the sum: 12 - 2 + 2 = 12.

Dot Product – The dot product of two vectors is calculated by multiplying their corresponding components and summing the results.
Vector Components – Understanding the individual components of vectors is essential for performing operations like the dot product.