Given vectors A = (2, -1, 3) and B = (4, 0, -2), find A × B.
Practice Questions
1 question
Q1
Given vectors A = (2, -1, 3) and B = (4, 0, -2), find A × B.
(-1, -10, 4)
(1, 10, -4)
(10, -1, 4)
(10, 1, -4)
A × B = |i j k|\n|2 -1 3|\n|4 0 -2| = (-1, -10, 4)
Questions & Step-by-step Solutions
1 item
Q
Q: Given vectors A = (2, -1, 3) and B = (4, 0, -2), find A × B.
Solution: A × B = |i j k|\n|2 -1 3|\n|4 0 -2| = (-1, -10, 4)
Steps: 11
Step 1: Write down the vectors A and B. A = (2, -1, 3) and B = (4, 0, -2).
Step 2: Set up the determinant for the cross product using the unit vectors i, j, k.
Step 3: Create a 3x3 matrix with the first row as the unit vectors (i, j, k), the second row as the components of vector A, and the third row as the components of vector B.
Step 4: The matrix looks like this: | i j k |
Step 5: | 2 -1 3 |
Step 6: | 4 0 -2 |
Step 7: Calculate the determinant using the formula for the cross product.
Step 8: For the i component, calculate: (-1 * -2) - (3 * 0) = 2.
Step 9: For the j component, calculate: -(2 * -2 - 3 * 4) = -(-4 - 12) = 16.
Step 10: For the k component, calculate: (2 * 0) - (-1 * 4) = 0 + 4 = 4.
Step 11: Combine the components to get the result: A × B = (2, 16, 4).
