If E = (2, -1, 3) and F = (1, 2, 0), what is E · F?

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Question: If E = (2, -1, 3) and F = (1, 2, 0), what is E · F?

Options:

Correct Answer: -1

Solution:

E · F = 2*1 + (-1)*2 + 3*0 = 2 - 2 + 0 = 0.

If E = (2, -1, 3) and F = (1, 2, 0), what is E · F?

If E = (2, -1, 3) and F = (1, 2, 0), what is E · F?

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

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