If A = (1, 0, 0) and B = (0, 1, 0), what is the value of A · B?

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Question: If A = (1, 0, 0) and B = (0, 1, 0), what is the value of A · B?

Options:

Correct Answer: 0

Solution:

A · B = 1*0 + 0*1 + 0*0 = 0.

If A = (1, 0, 0) and B = (0, 1, 0), what is the value of A · B?

If A = (1, 0, 0) and B = (0, 1, 0), what is the value of A · B?

Step 1: Identify the components of vector A, which are (1, 0, 0). This means A has three components: A1 = 1, A2 = 0, A3 = 0.
Step 2: Identify the components of vector B, which are (0, 1, 0). This means B has three components: B1 = 0, B2 = 1, B3 = 0.
Step 3: Use the formula for the dot product of two vectors: A · B = A1 * B1 + A2 * B2 + A3 * B3.
Step 4: Substitute the values into the formula: A · B = 1 * 0 + 0 * 1 + 0 * 0.
Step 5: Calculate each part: 1 * 0 = 0, 0 * 1 = 0, and 0 * 0 = 0.
Step 6: Add the results together: 0 + 0 + 0 = 0.
Step 7: Conclude that the value of A · B is 0.

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