If A = (1, 1, 1) and B = (2, 2, 2), what is A × B?
Practice Questions
Q1
If A = (1, 1, 1) and B = (2, 2, 2), what is A × B?
(0, 0, 0)
(1, 1, 1)
(2, 2, 2)
(3, 3, 3)
Questions & Step-by-Step Solutions
If A = (1, 1, 1) and B = (2, 2, 2), what is A × B?
Correct Answer: (0, 0, 0)
Step 1: Identify the vectors A and B. A = (1, 1, 1) and B = (2, 2, 2).
Step 2: Check if the vectors A and B are parallel. Two vectors are parallel if one is a scalar multiple of the other.
Step 3: Notice that B is 2 times A (B = 2 * A). This means A and B are parallel.
Step 4: Understand that the cross product of two parallel vectors is always (0, 0, 0).
Step 5: Therefore, calculate A × B = (0, 0, 0).
Vector Cross Product – The cross product of two vectors results in a vector that is perpendicular to both, and is only defined for non-parallel vectors.
Parallel Vectors – Two vectors are parallel if they are scalar multiples of each other, which results in a cross product of zero.
