If A = 1i + 1j + 1k and B = 1i + 2j + 3k, what is A · B?

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Question: If A = 1i + 1j + 1k and B = 1i + 2j + 3k, what is A · B?

Options:

Correct Answer: 5

Solution:

A · B = (1)(1) + (1)(2) + (1)(3) = 1 + 2 + 3 = 6.

If A = 1i + 1j + 1k and B = 1i + 2j + 3k, what is A · B?

If A = 1i + 1j + 1k and B = 1i + 2j + 3k, what is A · B?

Step 1: Identify the components of vector A. A = 1i + 1j + 1k means A has components: A_x = 1, A_y = 1, A_z = 1.
Step 2: Identify the components of vector B. B = 1i + 2j + 3k means B has components: B_x = 1, B_y = 2, B_z = 3.
Step 3: Use the formula for the dot product A · B, which is A · B = (A_x * B_x) + (A_y * B_y) + (A_z * B_z).
Step 4: Substitute the values into the formula: A · B = (1 * 1) + (1 * 2) + (1 * 3).
Step 5: Calculate each multiplication: (1 * 1) = 1, (1 * 2) = 2, (1 * 3) = 3.
Step 6: Add the results together: 1 + 2 + 3 = 6.

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