If the scalar product of vectors A = (x, y, z) and B = (2, -1, 3) is 10, what is

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Question: If the scalar product of vectors A = (x, y, z) and B = (2, -1, 3) is 10, what is the equation?

Options:

Correct Answer: 2x - y + 3z = 10

Solution:

A · B = 2x - y + 3z = 10.

If the scalar product of vectors A = (x, y, z) and B = (2, -1, 3) is 10, what is the equation?

If the scalar product of vectors A = (x, y, z) and B = (2, -1, 3) is 10, what is the equation?

Correct Answer: 2x - y + 3z = 10

Step 1: Understand that the scalar product (also called the dot product) of two vectors A and B is calculated by multiplying their corresponding components and then adding those products together.
Step 2: Identify the components of vector A, which are (x, y, z), and the components of vector B, which are (2, -1, 3).
Step 3: Write the formula for the scalar product: A · B = (x * 2) + (y * -1) + (z * 3).
Step 4: Simplify the expression: A · B = 2x - y + 3z.
Step 5: Set the scalar product equal to 10, as given in the question: 2x - y + 3z = 10.

Scalar Product – The scalar product (or dot product) of two vectors is calculated by multiplying their corresponding components and summing the results.
Vector Components – Understanding how to represent vectors in component form and how to manipulate these components in equations.