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Byte of Accounting, Inc.General JournalNeed help with 27 through.pdf

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By Expressing diagonals as vectors, and using the definition of the dot product, find the smaller angle between any two diagonals of a cube, where each diagonal connects diametrically opposite corners and passes through the center of the cube. Solution vectors of diagonal will be from (0,0,0) to (a,a,a) d1 = ai +aj + ak from( a,0,0) to (0,a,a) d2 = -ai + aj + ak cos = d1 . d2 / { |d1| |d2| } d1.d2 = -a^2 + a^2 + a^2 =a^2 |d1| = 3 a |d2| = 3 a cos = a^2 /3 a^2 = 1/3 = cos-1(1/3).

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Byte of Accounting, Inc.General JournalNeed help with 27 through.pdfajantha11

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- By Expressing diagonals as vectors, and using the definition of the dot product, find the smaller angle between any two diagonals of a cube, where each diagonal connects diametrically opposite corners and passes through the center of the cube. Solution vectors of diagonal will be from (0,0,0) to (a,a,a) d1 = ai +aj + ak from( a,0,0) to (0,a,a) d2 = -ai + aj + ak cos = d1 . d2 / { |d1| |d2| } d1.d2 = -a^2 + a^2 + a^2 =a^2 |d1| = 3 a |d2| = 3 a cos = a^2 /3 a^2 = 1/3 = cos-1(1/3)