If A = (2, 3, 4) and B = (1, 0, -1), find the vector product A × B.
Practice Questions
1 question
Q1
If A = (2, 3, 4) and B = (1, 0, -1), find the vector product A × B.
(3, 6, -3)
(3, 4, -3)
(3, -4, 6)
(3, -6, 4)
A × B = |i j k|\n|2 3 4|\n|1 0 -1| = (3, 6, -3)
Questions & Step-by-step Solutions
1 item
Q
Q: If A = (2, 3, 4) and B = (1, 0, -1), find the vector product A × B.
Solution: A × B = |i j k|\n|2 3 4|\n|1 0 -1| = (3, 6, -3)
Steps: 11
Step 1: Write down the vectors A and B. A = (2, 3, 4) and B = (1, 0, -1).
Step 2: Set up the determinant for the vector product A × B 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 (2, 3, 4), and the third row as the components of vector B (1, 0, -1).
Step 4: The matrix looks like this: | i j k |
Step 5: | 2 3 4 |
Step 6: | 1 0 -1 |
Step 7: Calculate the determinant of this matrix to find the vector product.
Step 8: Use the formula for the determinant: A × B = i(3 * -1 - 4 * 0) - j(2 * -1 - 4 * 1) + k(2 * 0 - 3 * 1).
