find the angle between force f=3i+4j-5k and displacement d=5i+4j+3k.also find the projection on f and d.
 

Asked by thakursonali2000 | 12th Aug, 2015, 07:44: PM

Expert Answer:

begin mathsize 12px style Given colon force comma stack space straight f with rightwards arrow on top equals 3 straight i with hat on top plus 4 straight j with hat on top minus 5 straight k with hat on top Displacement comma space straight d with rightwards arrow on top equals 5 straight i with hat on top plus 4 straight j with hat on top plus 3 straight k with hat on top Angle space between space two space vector space is space given space as comma cos space straight theta space equals fraction numerator stack space straight f with rightwards arrow on top. straight d with rightwards arrow on top over denominator fd end fraction stack space straight f with rightwards arrow on top. straight d with rightwards arrow on top equals open parentheses 3 straight i with hat on top plus 4 straight j with hat on top minus 5 straight k with hat on top close parentheses open parentheses 5 straight i with hat on top plus 4 straight j with hat on top plus 3 straight k with hat on top close parentheses space equals space 15 plus 16 minus 15 space equals space 16 fd space equals space open parentheses square root of 3 squared plus 4 squared plus left parenthesis negative 5 right parenthesis squared end root close parentheses open parentheses square root of 5 squared plus 4 squared plus left parenthesis 3 right parenthesis squared end root close parentheses equals open parentheses square root of 9 plus 16 plus 25 end root close parentheses open parentheses square root of 25 plus 16 plus 9 end root close parentheses space equals space 50 Therefore comma space cos space straight theta space space equals space 16 over 50 space equals space 0.32 straight theta equals space cos to the power of negative 1 end exponent space left parenthesis 0.32 right parenthesis space equals space 71.33 degree  To space find space the space pojection space of space straight f space on space straight d comma fcos space straight theta space equals space square root of 50 space cross times space 0.32 space equals space 2.26 space straight N space end style

Answered by Priyanka Kumbhar | 13th Aug, 2015, 09:11: AM

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