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k= (0,0,1) j+k 1 1 i = (1,0,0) j= (0, 1,0) Notice the illusion Is (0, 0, 0) a top or a bottom corner? Figure 1.4: Unit cube from i, j, k and twelve clock vectors. 2:00

k= (0,0,1) j+k 1 1 i = (1,0,0) j= (0, 1,0) Notice the illusion Is (0, 0, 0) a top or a bottom corner? Figure 1.4: Unit cube from i, j, k and twelve clock vectors. 2:00

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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Question about special vectors on cubes and clocks in the figure 1.4 attached.

A. Which point of the cube is i + j? Which point is the vector sum of i = (1, 0, 0) and j = (0,1,0) and k = (0,0,1)? Describe all points (x,y,z) in the cube.

B. In xyz space, where is the plane of all linear combinations of i = (1,0,0) and i +j = (1,1,0)?

k = (0,0,1) j+k i = (1, 0, 0) j= (0, 1, 0) Notice the illusion Is (0,0,0) a top or a bottom corner? Figure 1.4: Unit cube from i, j, k and twelve clock vectors. 2:00
Transcribed Image Text:k = (0,0,1) j+k i = (1, 0, 0) j= (0, 1, 0) Notice the illusion Is (0,0,0) a top or a bottom corner? Figure 1.4: Unit cube from i, j, k and twelve clock vectors. 2:00
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