What is the cross product of u = (1, 2, 3) and v = (4, 5, 6)?
Practice Questions
1 question
Q1
What is the cross product of u = (1, 2, 3) and v = (4, 5, 6)?
(-3, 6, -3)
(0, 0, 0)
(3, -6, 3)
(1, 2, 3)
u × v = |i j k| |1 2 3| |4 5 6| = (-3, 6, -3)
Questions & Step-by-step Solutions
1 item
Q
Q: What is the cross product of u = (1, 2, 3) and v = (4, 5, 6)?
Solution: u × v = |i j k| |1 2 3| |4 5 6| = (-3, 6, -3)
Steps: 5
Step 1: Write down the vectors u and v. Here, u = (1, 2, 3) and v = (4, 5, 6).
Step 2: Set up a 3x3 determinant using the unit vectors i, j, k and the components of u and v. It looks like this: |i j k| |1 2 3| |4 5 6|.
Step 3: Calculate the determinant. This involves finding the value of the determinant using the formula: i*(2*6 - 3*5) - j*(1*6 - 3*4) + k*(1*5 - 2*4).
