Created on 2024-06-20Asked by Ethan Thompson (Solvelet student)
Compute the cross product of the vectors u=⟨2,−3,4⟩ and v=⟨−1,5,2⟩.
Solution
Step 1: Identify the vectors u=⟨2,−3,4⟩ and v=⟨−1,5,2⟩. Step 2: Use the formula for the cross product of two vectors: u×v=∣∣ijk2−34−152∣∣. Step 3: Expand the determinant along the top row: u×v=i∣∣−3452∣∣−j∣∣24−12∣∣+k∣∣2−3−15∣∣. Step 4: Compute the determinants: u×v=i((−3)(2)−(4)(5))−j((2)(2)−(4)(−1))+k((2)(5)−(−3)(−1)). Step 5: Perform the calculations: u×v=i(−6−20)−j(4+4)+k(10−3). Step 6: Simplify: u×v=−26i−8j+13k. Step 7: Conclusion. The cross product of u and v is u×v=⟨−26,−8,13⟩. Solved on Solvelet with Basic AI Model
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DefinitionA vector product is a function of two vectors whose values are also vectors. Additionally, in the cross product, the vectors are perpendicular to the plane formed by the two vectors. The value of the length product is equal to the area of the parallelogram represented by two vectors also pointing to the right.
