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At what angle should two force vectors 2f and √2f act so that the resultant force is √10f

Asked by rorshack24 14th July 2019, 9:49 AM
Answered by Expert
Let a and b are two vectors making angle θ as shown in figure. Resultant of two vectors are givn by law of parallelogram.
Hence Diagonal OC is resultant a+b.
Angle Φ in the figure is calculated from ΔOAC using law of cosines as :-
 begin mathsize 14px style open vertical bar a with rightwards arrow on top plus space b with rightwards arrow on top close vertical bar space equals space square root of a squared plus b squared minus 2 a b space cos capital phi end root end style .....................(1)
by substituting |a| = 2   and |b| = √2   and  | a+b| = √10 , we get Φ = cos-1[ (-10+4+2)/(2×2×√2) ] = 135°
Hence angle between two force vectors of magnitude 2f and √2f = 180 -135 = 45°
Answered by Expert 14th July 2019, 4:22 PM
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