Find the scalar product of the vectors G = (2, -3, 1) and H = (4, 0, -2).

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Question: Find the scalar product of the vectors G = (2, -3, 1) and H = (4, 0, -2).

Options:

Correct Answer: -2

Solution:

G · H = 2*4 + (-3)*0 + 1*(-2) = 8 + 0 - 2 = 6.

Find the scalar product of the vectors G = (2, -3, 1) and H = (4, 0, -2).

Find the scalar product of the vectors G = (2, -3, 1) and H = (4, 0, -2).

Step 1: Identify the components of vector G, which are (2, -3, 1).
Step 2: Identify the components of vector H, which are (4, 0, -2).
Step 3: Multiply the first component of G (2) by the first component of H (4). This gives 2 * 4 = 8.
Step 4: Multiply the second component of G (-3) by the second component of H (0). This gives -3 * 0 = 0.
Step 5: Multiply the third component of G (1) by the third component of H (-2). This gives 1 * -2 = -2.
Step 6: Add the results from Steps 3, 4, and 5 together: 8 + 0 - 2.
Step 7: Calculate the final result: 8 + 0 - 2 = 6.

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