If the vector a = (2, 3) and b = (4, 1), what is the cross product a × b?

If the vector a = (2, 3) and b = (4, 1), what is the cross product a × b?

Step 1: Identify the components of vector a. Here, a = (2, 3), so the first component is 2 and the second component is 3.
Step 2: Identify the components of vector b. Here, b = (4, 1), so the first component is 4 and the second component is 1.
Step 3: Use the formula for the cross product of two 2D vectors a = (x1, y1) and b = (x2, y2). The formula is a × b = x1*y2 - y1*x2.
Step 4: Substitute the values into the formula. Here, x1 = 2, y1 = 3, x2 = 4, and y2 = 1.
Step 5: Calculate the first part of the formula: 2 * 1 = 2.
Step 6: Calculate the second part of the formula: 3 * 4 = 12.
Step 7: Subtract the second part from the first part: 2 - 12 = -10.
Step 8: The result of the cross product a × b is -10.

Cross Product of Vectors – The cross product is a binary operation on two vectors in three-dimensional space, resulting in a vector that is perpendicular to both. However, in two dimensions, the cross product can be computed as a scalar value representing the magnitude of the vector perpendicular to the plane formed by the two vectors.