If llvll=5 and llwll=3, what are the smallest and largest values of llv-wll? What are the smallest and largest values of v*w?

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If llvll=5 and llwll=3,

a) the smallest value of llv-wll is 5-3=2, which happens when v and w are parallel.

b) the largest value of llv-wll is 5+3=8, which happens when v and w are anti-parallel.

c) the smallest value of v*w is 5*3*(-1)=-15, which happens when v and w are anti-parallel (cos 180°=-1).

d) the largest value of v*w is 5*3*(1)=15, which happens when v and w are parallel (cos 0°= 1).

Remember that v*w= llvll llwll cosθ, and abs(cosθ)≤1.

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