If A = (1, 2, 3) and B = (0, 1, 0), what is the direction of the vector product
Practice Questions
Q1
If A = (1, 2, 3) and B = (0, 1, 0), what is the direction of the vector product A × B?
(2, -3, 1)
(3, 0, -1)
(1, 0, -1)
(1, 3, 0)
Questions & Step-by-Step Solutions
If A = (1, 2, 3) and B = (0, 1, 0), what is the direction of the vector product A × B?
Correct Answer: (2, -3, 1)
Step 1: Identify the vectors A and B. A = (1, 2, 3) and B = (0, 1, 0).
Step 2: Use the formula for the vector product (cross product) A × B. The formula is: A × B = (A2*B3 - A3*B2, A3*B1 - A1*B3, A1*B2 - A2*B1).
Step 3: Substitute the values from vectors A and B into the formula.
Step 4: Calculate each component: First component: 2*0 - 3*1 = 0 - 3 = -3. Second component: 3*0 - 1*0 = 0 - 0 = 0. Third component: 1*1 - 2*0 = 1 - 0 = 1.
Step 5: Combine the components to get the vector product A × B = (0, -3, 1).
Step 6: The direction of the vector product A × B is given by the resulting vector (0, -3, 1).
Vector Product – The vector product (or cross product) of two vectors results in a vector that is perpendicular to both original vectors, with a direction determined by the right-hand rule.
Direction of Vectors – Understanding how to determine the direction of the resulting vector from the cross product, including the use of coordinate systems.
