If A = (1, 1, 1) and B = (x, y, z) such that A · B = 3, what is the value of x +

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Question: If A = (1, 1, 1) and B = (x, y, z) such that A · B = 3, what is the value of x + y + z?

Options:

Correct Answer: 3

Solution:

A · B = 1*x + 1*y + 1*z = x + y + z = 3.

If A = (1, 1, 1) and B = (x, y, z) such that A · B = 3, what is the value of x + y + z?

If A = (1, 1, 1) and B = (x, y, z) such that A · B = 3, what is the value of x + y + z?

Step 1: Identify the vectors A and B. A = (1, 1, 1) and B = (x, y, z).
Step 2: Understand that A · B means the dot product of A and B.
Step 3: Calculate the dot product A · B using the formula: A · B = A1*B1 + A2*B2 + A3*B3.
Step 4: Substitute the values from A and B into the formula: A · B = 1*x + 1*y + 1*z.
Step 5: Simplify the expression: A · B = x + y + z.
Step 6: We know from the question that A · B = 3.
Step 7: Set the equation x + y + z = 3.
Step 8: The value of x + y + z is therefore 3.

Dot Product – The dot product of two vectors A and B is calculated by multiplying corresponding components and summing the results.
Vector Components – Understanding how to represent vectors in component form and how to manipulate these components in equations.