What is the cross product of the vectors (1, 0, 0) and (0, 1, 0)?
Practice Questions
Q1
What is the cross product of the vectors (1, 0, 0) and (0, 1, 0)?
(0, 0, 1)
(1, 1, 0)
(0, 0, 0)
(1, 0, 0)
Questions & Step-by-Step Solutions
What is the cross product of the vectors (1, 0, 0) and (0, 1, 0)?
Step 1: Identify the two vectors. The first vector is (1, 0, 0) and the second vector is (0, 1, 0).
Step 2: Write down the formula for the cross product of two vectors A = (a1, a2, a3) and B = (b1, b2, b3). The formula is: A × B = (a2*b3 - a3*b2, a3*b1 - a1*b3, a1*b2 - a2*b1).
Step 3: Substitute the values from the vectors into the formula. Here, A = (1, 0, 0) and B = (0, 1, 0). So, a1 = 1, a2 = 0, a3 = 0, b1 = 0, b2 = 1, b3 = 0.
Step 4: Calculate each component of the cross product using the formula.
Component 1: a2*b3 - a3*b2 = 0*0 - 0*1 = 0.
Component 2: a3*b1 - a1*b3 = 0*0 - 1*0 = 0.
Component 3: a1*b2 - a2*b1 = 1*1 - 0*0 = 1.
Step 5: Combine the components to get the final result. The cross product is (0, 0, 1).
