If C = (3, -1, 2) and D = (0, 4, -3), what is the value of C · D?

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Question: If C = (3, -1, 2) and D = (0, 4, -3), what is the value of C · D?

Options:

Correct Answer: -10

Solution:

C · D = 3*0 + (-1)*4 + 2*(-3) = 0 - 4 - 6 = -10.

If C = (3, -1, 2) and D = (0, 4, -3), what is the value of C · D?

If C = (3, -1, 2) and D = (0, 4, -3), what is the value of 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 (0, 4, -3).
Step 3: Multiply the first component of C (3) by the first component of D (0). This gives 3 * 0 = 0.
Step 4: Multiply the second component of C (-1) by the second component of D (4). This gives -1 * 4 = -4.
Step 5: Multiply the third component of C (2) by the third component of D (-3). This gives 2 * -3 = -6.
Step 6: Add the results from Steps 3, 4, and 5 together: 0 + (-4) + (-6).
Step 7: Calculate the sum: 0 - 4 - 6 = -10.

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 crucial for performing operations like the dot product.