Answered: Given two vectors Á = 4î + 3j and B =…

Given two vectors Á = 4î + 3j and B = 12î – 5j a)Find the scalar product A · B. b)Find the angle between the two vectors. c)Find the vector product A × B.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Vector A has a magnitude of 4 m and lies in the xy plane directed at 45 degrees counterclockwise from the positive x axis, whereas the vector B has a magnitude of 3m and lies in the yz plane directed at 30 degrees from the positive z axic. Find the cross product A x B and the angle between the vectors.
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With the given three vector A, B, C. Determine the magnitude of the dot product of vectors AxC and CxB A= 2i - 3j + 4k B= -3i - 6j + 5k C= 4i + 2j
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Review I Constants Part A Vector A has magnitude 17.0 m and vector B has magnitude 17.0 m. The scalar product A· B is 119 m2. What is the magnitude of the vector product between these two vectors? Express your answer with the appropriate units. HẢ Ã x B = Value Units
"If vectors A = 2i + 5j + 2k and B = 5i + 2j + 2k, then the dot product A.B will be equal to" 24 14 40 12
Find the scalar and cross product of the two vectors shown in figure 27 using the component method.
E. Engagement Consider the vectors given below A = Azî + Ayĵ + A,k B = Bxî + Byj + B,k Get the dot product of A andB by following the steps below. A·B = (Azî + Ayĵ + A‚k)(Bxî + Byĵ + B,k) Step 1: Multiply the vectors, the way you multiply polynomials. You should get 9 terms. Ā ·B = Step 2: Rearrange your terms. Set side by side the components and the unit vector. A ·B = Step 3: Apply the dot products to your unit vectors. Recall: î · î = j· j = k · k = 1 and î ·j = î · k = j · k = 0 A·B =. Step 4: Write the simplified and the final dot product A·B =
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The scalar product of a and b is defined to be a x b = |a||b| sin 0.a O a. b = |a||b| cose.b ax b = |a||b|cos 0 .c a. b = O |a||b| sin 0 .d O
The Vector Product Two vectors lying in the xy-plane are given by the equations A = 8î + 2j and B = -3î + 3j. Find Ax B and verify that Ã ×B = -B x A. SOLUTION Conceptualize Given the unit-vector notations of the vectors, think about the directions the vectors point in space. Draw them on graph paper and imagine the parallelogram for these vectors. Categorize Because we use the definition of the cross product discussed in this section, we categorize this example as-Select-- problem. Write the cross product of the two vectors: AxB = î + 2j ) x î + 3j Perform the multiplication: ĀxB = 8î x (-3î) + 8î × 3j +| j x (-3î) + 2j x Use the equations for the cross product of unit vectors to evaluate the various terms: AXB = To verify that AxB = -B x A, evaluate Bx A: BxA = (-31 + Perform the multiplication: BxA = (-31) x ]î +(-3î) × 2j + 3ĵ × 8î + j x 2j Use the equations for the cross product of unit vectors evaluate the various terms: BxA = Therefore, Ax B = -B xA As an alternative method for…