If u = (2, 3, 1) and v = (1, 0, -1), find the dot product u · v.

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Question: If u = (2, 3, 1) and v = (1, 0, -1), find the dot product u · v.

Options:

Correct Answer: 5

Solution:

u · v = 2*1 + 3*0 + 1*(-1) = 2 + 0 - 1 = 1.

If u = (2, 3, 1) and v = (1, 0, -1), find the dot product u · v.

If u = (2, 3, 1) and v = (1, 0, -1), find the dot product u · v.

Correct Answer: 1

Step 1: Identify the components of vector u, which are (2, 3, 1).
Step 2: Identify the components of vector v, which are (1, 0, -1).
Step 3: Multiply the first component of u (2) by the first component of v (1). This gives 2 * 1 = 2.
Step 4: Multiply the second component of u (3) by the second component of v (0). This gives 3 * 0 = 0.
Step 5: Multiply the third component of u (1) by the third component of v (-1). This gives 1 * -1 = -1.
Step 6: Add the results from Steps 3, 4, and 5 together: 2 + 0 - 1.
Step 7: Calculate the final result: 2 + 0 = 2, then 2 - 1 = 1.

Dot Product – The dot product of two vectors is calculated by multiplying their corresponding components and summing the results.