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

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

Options:

Correct Answer: 5

Solution:

Cross product in 2D = a1*b2 - a2*b1 = 2*3 - (-1)*1 = 6 + 1 = 7

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

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

Step 1: Identify the components of vector a. Here, a = (2, -1) means a1 = 2 and a2 = -1.
Step 2: Identify the components of vector b. Here, b = (1, 3) means b1 = 1 and b2 = 3.
Step 3: Use the formula for the cross product in 2D, which is a1 * b2 - a2 * b1.
Step 4: Substitute the values into the formula: 2 * 3 - (-1) * 1.
Step 5: Calculate 2 * 3, which equals 6.
Step 6: Calculate -(-1) * 1, which equals 1.
Step 7: Add the results from Step 5 and Step 6: 6 + 1 = 7.
Step 8: The final result of the cross product a × b is 7.

Cross Product in 2D – The cross product of two vectors in 2D is calculated using the formula a1*b2 - a2*b1, which results in a scalar value.