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

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

Correct Answer: 3

Step 1: Understand that A = (x, y, z) is a vector with components x, y, and z.
Step 2: Understand that B = (2, 3, 4) is another vector with components 2, 3, and 4.
Step 3: The dot product A · B is calculated by multiplying corresponding components of A and B and then adding those products together.
Step 4: Write the equation for the dot product: A · B = x*2 + y*3 + z*4.
Step 5: Set the equation equal to 10, as given: x*2 + y*3 + z*4 = 10.
Step 6: Look for values of x, y, and z that satisfy this equation. One possible solution is x = 1, y = 1, z = 1.
Step 7: Calculate x + y + z using the found values: 1 + 1 + 1 = 3.

Dot Product – Understanding the dot product of two vectors and how to set up the equation based on given values.
Linear Equations – Solving for multiple variables in a linear equation derived from the dot product.