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Fundamentals of Stress and Vibration
[A Practical guide for aspiring Designers / Analysts] 1. Mathematics for Structural mechanics
ͳǤ͹ ‘™ –‘ ‹†‡–‹ˆ› ƒ ‹‰Š–- ƒ†‡† ‘‘”†‹ƒ–‡ •›•–‡

‘•‹†‡” –Š‡ ˆ‘ŽŽ‘™‹‰ ‡š’”‡••‹‘• ‘ˆ ˜‡ –‘” ’”‘†— –ǣ

i × j = k - - - - (1.37)
j × k = i - - - - (1.38)

k × i = j - - - - (1.39)
Let us graphically understand equation (1.37), (1.38) and (1.39) and verify whether the resultant
vector matches with the coordinate system, by the definition of vector product/ right-handed screw
principle.

[Fig 1.47: vector products for anti-clockwise rotations of coordinate axes]

‹‹Žƒ”Ž›ǡ ˆ‘” Ž‘ ™‹•‡ ”‘–ƒ–‹‘•ǡ ™‡ Šƒ˜‡ǣ

[Fig 1.48: vector products for clockwise rotations of coordinate axes]

‡ –‘”• ‘ˆ †‹ˆˆ‡”‡– ‹†•ǡ ™Š‡ —Ž–‹’Ž‹‡† Ž‡ƒ† –‘ ‹’‘”–ƒ– ”‡•—Ž–• ƒ† –Š‡ ˆ‘ŽŽ‘™‹‰ ‡“—ƒ–‹‘•
ƒ”‡ ‡‡†‡† –‘ •‘Ž˜‡ ƒ› ˆ—†ƒ‡–ƒŽ •‹–—ƒ–‹‘• ‹ ‡ Šƒ‹ •Ǥ

QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries,
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