Open Question
(I) Show that (b) î x ĵ, = k̂ , î x k̂ , = - ĵ , and ĵ x k̂ = î .
3. Vectors
Intro to Cross Product (Vector Product)
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Find the magnitude and direction of the vector C =2B × A.
A
|C| = 27; along the –x direction
B
|C| = 27; along the +x direction
C
|C| = 54; along the +x direction
D
|C| = 54; along the +y direction
E
|C| = 19; along the +x direction
Verified step by step guidance1
First, identify the vectors A and B from the image. Vector A is pointing in the -z direction with a magnitude of 9, and vector B is pointing in the +x direction with a magnitude of 3.
To find the vector C = 2B × A, first calculate the vector 2B. Since B is in the +x direction, 2B will also be in the +x direction with a magnitude of 6.
Next, perform the cross product 2B × A. The cross product of two vectors results in a vector that is perpendicular to both original vectors. Use the right-hand rule to determine the direction of the cross product.
Apply the right-hand rule: Point your fingers in the direction of 2B (along the +x axis), then curl them towards A (along the -z axis). Your thumb will point in the direction of the cross product, which is along the +y axis.
Calculate the magnitude of the cross product using the formula |C| = |2B| * |A| * sin(θ), where θ is the angle between the vectors. Since 2B and A are perpendicular, sin(θ) = 1. Therefore, |C| = 6 * 9 = 54.
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