Given vectors A = (x, y, z) and B = (1, 2, 3), if A · B = 14, what is the value
Practice Questions
Q1
Given vectors A = (x, y, z) and B = (1, 2, 3), if A · B = 14, what is the value of x + 2y + 3z?
14
10
8
6
Questions & Step-by-Step Solutions
Given vectors A = (x, y, z) and B = (1, 2, 3), if A · B = 14, what is the value of x + 2y + 3z?
Step 1: Identify the vectors A and B. A = (x, y, z) and B = (1, 2, 3).
Step 2: Understand that the dot product A · B is calculated by multiplying corresponding components of the vectors and then adding those products together.
Step 3: Write the formula for the dot product: A · B = x*1 + y*2 + z*3.
Step 4: Substitute the known value of the dot product: A · B = 14.
Step 5: Set up the equation: x*1 + y*2 + z*3 = 14.
Step 6: Recognize that the left side of the equation (x + 2y + 3z) is equal to 14.
Step 7: Conclude that x + 2y + 3z = 14.
Dot Product – The dot product of two vectors is calculated by multiplying their corresponding components and summing the results.
Vector Components – Understanding how to represent vectors in component form and how to manipulate these components in equations.
