For the vectors A = (1, 0, 0) and B = (0, 1, 0), what is the scalar product A ·

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Question: For the vectors A = (1, 0, 0) and B = (0, 1, 0), what is the scalar product A · B?

Options:

Correct Answer: 0

Solution:

A · B = 1*0 + 0*1 + 0*0 = 0.

For the vectors A = (1, 0, 0) and B = (0, 1, 0), what is the scalar product A · B?

For the vectors A = (1, 0, 0) and B = (0, 1, 0), what is the scalar product A · B?

Step 1: Identify the components of vector A, which are (1, 0, 0). This means A has x = 1, y = 0, and z = 0.
Step 2: Identify the components of vector B, which are (0, 1, 0). This means B has x = 0, y = 1, and z = 0.
Step 3: Use the formula for the scalar product (also known as the dot product), which is A · B = Ax * Bx + Ay * By + Az * Bz.
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 scalar product A · B is 0.

Scalar Product – The scalar product (or dot product) of two vectors is calculated by multiplying their corresponding components and summing the results.
Orthogonality – The result of the scalar product indicates whether the vectors are orthogonal; a result of zero means the vectors are perpendicular.