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a. We begin by defining the cross products using the vectors i, j, and k. Referring to Figure 9.4.1, explain why i, j, k in that order form a right- hand system. We then define i xj to be k- that is ix j = k. b. Now explain why i, k, and −j in that order form a right-hand system. We then define i xk to be -j- that is ix k = -j. c. Continuing in this way, complete the missing entries in Table 9.4.2. Table 9.4.2 Table of cross products involving i, j, and k. ixj=k ixk=-j jxk= jxi= kxi= kxj=

a. We begin by defining the cross products using the vectors i, j, and k. Referring to Figure 9.4.1, explain why i, j, k in that order form a right- hand system. We then define i xj to be k- that is ix j = k. b. Now explain why i, k, and −j in that order form a right-hand system. We then define i xk to be -j- that is ix k = -j. c. Continuing in this way, complete the missing entries in Table 9.4.2. Table 9.4.2 Table of cross products involving i, j, and k. ixj=k ixk=-j jxk= jxi= kxi= kxj=

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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9.4 The Cross Product Ak Figure 9.4.1 Basis vectors i, j, and k. Preview Activity 9.4.1 The cross product of two vectors, u and v, will itself be a vector denoted u x v. The direction of u x v is determined by the right- hand rule: if we point the index finger of our right hand in the direction of u and our middle finger in the direction of v, then our thumb points in the direction of u x v. a. We begin by defining the cross products using the vectors i, j, and k. Referring to Figure 9.4.1, explain why i, j, k in that order form a right- hand system. We then define i xj to be k- that is ixj=k. b. Now explain why i, k, and -j in that order form a right-hand system. We then define ix k to be -j- that is ix k-j. c. Continuing in this way, complete the missing entries in Table 9.4.2. Table 9.4.2 Table of cross products involving i, j, and k. ixj=k ixk=-j jxk= jxi= <xi= kx j =
Transcribed Image Text:9.4 The Cross Product Ak Figure 9.4.1 Basis vectors i, j, and k. Preview Activity 9.4.1 The cross product of two vectors, u and v, will itself be a vector denoted u x v. The direction of u x v is determined by the right- hand rule: if we point the index finger of our right hand in the direction of u and our middle finger in the direction of v, then our thumb points in the direction of u x v. a. We begin by defining the cross products using the vectors i, j, and k. Referring to Figure 9.4.1, explain why i, j, k in that order form a right- hand system. We then define i xj to be k- that is ixj=k. b. Now explain why i, k, and -j in that order form a right-hand system. We then define ix k to be -j- that is ix k-j. c. Continuing in this way, complete the missing entries in Table 9.4.2. Table 9.4.2 Table of cross products involving i, j, and k. ixj=k ixk=-j jxk= jxi= <xi= kx j =
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