Question

Find the work done and the projection of F on S when force F= (3i +4j-5k) unit and

displacement S= (5i+4j+3k) unit.​

Answer 1

Answer:

work done =16

Explanation:

w=F.S

(3i+4j-5k)(5i+4j+3k)

15(1)+16(1)-15(1)

15+16-15

=16

Answer 2

Answer:Given:

force, f⃗ =3T^+4j^−5k^

Displacement, d→=5T^+4j^+3k^

Angle between two vector is given as, cosθ=f⃗ ⋅d⃗ fd

f→⋅d→=(3i^+4j^−5k^)(5i^+4j^+3k^)=15+16−15=16

fd=(32+42+(−5)2−−−−−−−−−−−−√)(52+42+(3)2−−−−−−−−−−−√)

=(9+16+25−−−−−−−−−√)(25+16+9−−−−−−−−−√)=50

Therefore, cosθ=1650=0.32

θ=cos−1(0.32)=71.33∘

To find the pojection of f on d fcosθ=50−−√×0.32=2.26N

Explanation: