If A = (1, 2, 3) and B = (x, y, z) are such that A · B = 0, what is the conditio

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Question: If A = (1, 2, 3) and B = (x, y, z) are such that A · B = 0, what is the condition for x, y, z?

Options:

Correct Answer: x + 2y + 3z = 0

Solution:

A · B = 1*x + 2*y + 3*z = 0 gives the condition x + 2y + 3z = 0.

If A = (1, 2, 3) and B = (x, y, z) are such that A · B = 0, what is the condition for x, y, z?

If A = (1, 2, 3) and B = (x, y, z) are such that A · B = 0, what is the condition for x, y, z?

Step 1: Understand that A and B are vectors. A = (1, 2, 3) and B = (x, y, z).
Step 2: The dot product of two vectors A and B is calculated by multiplying their corresponding components and adding the results.
Step 3: For vectors A and B, the dot product A · B is calculated as: 1*x + 2*y + 3*z.
Step 4: We know from the question that A · B = 0, which means: 1*x + 2*y + 3*z = 0.
Step 5: Rearranging the equation gives us the condition: x + 2y + 3z = 0.
Step 6: This equation (x + 2y + 3z = 0) is the condition that x, y, and z must satisfy.

Dot Product – The dot product of two vectors A and B is calculated by multiplying corresponding components and summing the results.
Orthogonality – Two vectors are orthogonal (perpendicular) if their dot product equals zero.