What is the cross product of vectors (1, 2, 3) and (4, 5, 6)?
Practice Questions
Q1
What is the cross product of vectors (1, 2, 3) and (4, 5, 6)?
(-3, 6, -3)
(0, 0, 0)
(3, -6, 3)
(1, 2, 3)
Questions & Step-by-Step Solutions
What is the cross product of vectors (1, 2, 3) and (4, 5, 6)?
Step 1: Write down the vectors. We have vector A = (1, 2, 3) and vector B = (4, 5, 6).
Step 2: Set up the determinant using the unit vectors i, j, k. This looks like: |i j k| |1 2 3| |4 5 6|.
Step 3: Expand the determinant. This means we will calculate it using the formula: i*(2*6 - 3*5) - j*(1*6 - 3*4) + k*(1*5 - 2*4).
Step 4: Calculate each part: For i, we get 2*6 - 3*5 = 12 - 15 = -3. For j, we get 1*6 - 3*4 = 6 - 12 = -6, but we subtract this, so it becomes +6. For k, we get 1*5 - 2*4 = 5 - 8 = -3.
Step 5: Combine the results. The cross product is (-3, 6, -3).
