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Fundamentals of Stress and Vibration
[A Practical guide for aspiring Designers / Analysts] 1. Mathematics for Structural mechanics
Example: let us consider two vectors ( a ) and ( b ), in the ‘x-y’ plane. Find the magnitude and
direction of the vector resulting from subtraction of vector ( b ) from ( a )
[Fig 1.31: Vectors on an ‘x-y’ plane]
Since the vectors are fully defined, the resultant vector, is the difference of the vectors, and is given
by:
a − b = 4i + 5j − 7i + 2j = −3i + 3j
The magnitude of the resultant vector is: 3 + 3 = 3 2
2
2
The direction of the resultant vector is given by:
3
−1
0
tan −1 = tan −1 = 135 , with respect to the positive (x − axis)
−3
Let us now represent the magnitude and direction of the resultant graphically, [Fig 1.34]:
[Fig 1.34: Magnitude and direction of the resultant vector]
QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries,
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