Find the cross product of vectors A = (1, 2, 3) and B = (4, 5, 6).
Practice Questions
1 question
Q1
Find the cross product of vectors A = (1, 2, 3) and B = (4, 5, 6).
(-3, 6, -3)
(0, 0, 0)
(3, -6, 3)
(1, -2, 1)
Cross product A × B = |i j k| |1 2 3| |4 5 6| = (-3, 6, -3).
Questions & Step-by-step Solutions
1 item
Q
Q: Find the cross product of vectors A = (1, 2, 3) and B = (4, 5, 6).
Solution: Cross product A × B = |i j k| |1 2 3| |4 5 6| = (-3, 6, -3).
Steps: 7
Step 1: Write down the vectors A and B. A = (1, 2, 3) and B = (4, 5, 6).
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 | | 1 2 3 | | 4 5 6 |.
Step 5: Calculate the determinant of this matrix. This involves finding the determinant using the formula: i*(2*6 - 3*5) - j*(1*6 - 3*4) + k*(1*5 - 2*4).
Step 6: Simplify each part: i*(-3) - j*(-6) + k*(-3).
Step 7: Combine the results to get the final vector: (-3, 6, -3).
