Question: If the vector a = (3, 4) and b = (1, 2), find the cross product a × b.
Options:
-2
2
0
1
Correct Answer: -2
Solution:
In 2D, a × b = a1*b2 - a2*b1 = 3*2 - 4*1 = 6 - 4 = 2.
If the vector a = (3, 4) and b = (1, 2), find the cross product a × b.
Practice Questions
Q1
If the vector a = (3, 4) and b = (1, 2), find the cross product a × b.
-2
2
0
1
Questions & Step-by-Step Solutions
If the vector a = (3, 4) and b = (1, 2), find the cross product a × b.
Correct Answer: 2
Step 1: Identify the components of vector a. Here, a = (3, 4) means a1 = 3 and a2 = 4.
Step 2: Identify the components of vector b. Here, b = (1, 2) means b1 = 1 and b2 = 2.
Step 3: Use the formula for the cross product in 2D, which is a × b = a1 * b2 - a2 * b1.
Step 4: Substitute the values into the formula: a × b = 3 * 2 - 4 * 1.
Step 5: Calculate 3 * 2, which equals 6.
Step 6: Calculate 4 * 1, which equals 4.
Step 7: Subtract the second result from the first: 6 - 4 = 2.
Step 8: The final result of the cross product a × b is 2.
Cross Product in 2D – The cross product of two vectors in 2D can be calculated using the formula a × b = a1*b2 - a2*b1, which gives a scalar result.
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