If A = (a, b, c) and B = (1, 2, 3), and A · B = 14, find a + b + c.

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Question: If A = (a, b, c) and B = (1, 2, 3), and A · B = 14, find a + b + c.

Options:

Correct Answer: 7

Solution:

a*1 + b*2 + c*3 = 14. One possible solution is a = 2, b = 4, c = 0, so a + b + c = 6.

If A = (a, b, c) and B = (1, 2, 3), and A · B = 14, find a + b + c.

If A = (a, b, c) and B = (1, 2, 3), and A · B = 14, find a + b + c.

Correct Answer: 6

Step 1: Understand that A = (a, b, c) and B = (1, 2, 3).
Step 2: Recognize that A · B means we need to multiply corresponding elements of A and B and then add them together.
Step 3: Write the equation for the dot product: a*1 + b*2 + c*3 = 14.
Step 4: Simplify the equation to: a + 2b + 3c = 14.
Step 5: Find values for a, b, and c that satisfy this equation. One possible solution is a = 2, b = 4, c = 0.
Step 6: Calculate a + b + c using the values found: 2 + 4 + 0 = 6.

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 and recognizing that there can be multiple solutions.