Calculate the scalar product of the vectors (1, 0, 0) and (0, 1, 0).

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Question: Calculate the scalar product of the vectors (1, 0, 0) and (0, 1, 0).

Options:

Correct Answer: 0

Solution:

Scalar product = 1*0 + 0*1 + 0*0 = 0.

Calculate the scalar product of the vectors (1, 0, 0) and (0, 1, 0).

Calculate the scalar product of the vectors (1, 0, 0) and (0, 1, 0).

Step 1: Identify the two vectors. The first vector is (1, 0, 0) and the second vector is (0, 1, 0).
Step 2: Write down the formula for the scalar product (also known as the dot product). The formula is: a1*b1 + a2*b2 + a3*b3, where (a1, a2, a3) are the components of the first vector and (b1, b2, b3) are the components of the second vector.
Step 3: Substitute the components of the vectors into the formula. For the first vector (1, 0, 0), a1 = 1, a2 = 0, a3 = 0. For the second vector (0, 1, 0), b1 = 0, b2 = 1, b3 = 0.
Step 4: Calculate each part of the formula: 1*0 (which is 0), 0*1 (which is 0), and 0*0 (which is 0).
Step 5: Add the results from Step 4 together: 0 + 0 + 0 = 0.
Step 6: The scalar product of the vectors (1, 0, 0) and (0, 1, 0) 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 vectors (1, 0, 0) and (0, 1, 0) are orthogonal, meaning their scalar product is zero.