If A = (x, y, z) and B = (2, 3, 4), find the value of x if A · B = 10.

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Question: If A = (x, y, z) and B = (2, 3, 4), find the value of x if A · B = 10.

Options:

Correct Answer: 2

Solution:

A · B = x*2 + y*3 + z*4 = 10. If y = 0 and z = 0, then x = 5.

If A = (x, y, z) and B = (2, 3, 4), find the value of x if A · B = 10.

If A = (x, y, z) and B = (2, 3, 4), find the value of x if A · B = 10.

Step 1: Understand that A is a vector represented by (x, y, z) and B is a vector represented by (2, 3, 4).
Step 2: The dot product A · B is calculated by multiplying corresponding components of A and B and then adding those products together.
Step 3: Write the formula for the dot product: A · B = x*2 + y*3 + z*4.
Step 4: Set the equation equal to 10, since we know A · B = 10: x*2 + y*3 + z*4 = 10.
Step 5: To find the value of x, we need to simplify the equation. Assume y = 0 and z = 0 for simplicity.
Step 6: Substitute y and z into the equation: x*2 + 0*3 + 0*4 = 10.
Step 7: This simplifies to 2x = 10.
Step 8: Solve for x by dividing both sides of the equation by 2: x = 10 / 2.
Step 9: Calculate the result: x = 5.

Dot Product – The dot product of two vectors A and B is calculated by multiplying their corresponding components and summing the results.
Variable Isolation – Isolating a variable in an equation to solve for its value based on given conditions.