If u = (1, 2) and v = (3, 4), what is the dot product u · v?

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Question: If u = (1, 2) and v = (3, 4), what is the dot product u · v?

Options:

Correct Answer: 10

Solution:

Dot product u · v = 1*3 + 2*4 = 3 + 8 = 11.

If u = (1, 2) and v = (3, 4), what is the dot product u · v?

If u = (1, 2) and v = (3, 4), what is the dot product u · v?

Step 1: Identify the components of vector u, which are 1 and 2.
Step 2: Identify the components of vector v, which are 3 and 4.
Step 3: Multiply the first component of u (1) by the first component of v (3). This gives you 1 * 3 = 3.
Step 4: Multiply the second component of u (2) by the second component of v (4). This gives you 2 * 4 = 8.
Step 5: Add the results from Step 3 and Step 4 together. This gives you 3 + 8 = 11.
Step 6: The final result, which is the dot product u · v, is 11.

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