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Answer from: Quest
the value of v.w= -12.
step-by-step explanation:
we are given three vector r,v and w as:
r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>
we know that r,v and w could also be represented as:
r=5i-5j-2k
v=2i-8j-8k
and w= -2i+6j-5k
where i,j and k are the unit vectors of x,y and z-axis respectively.
also we know that it has the following property:
i.i=1 ; j.j=1; k.k=1
and i.=j.i=i.k=k.i=j.k=k.j=0
i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.
hence, v.w= (2i-8j- -2i+6j-5k)
= 2×(-2)+(-8)×(6)+(-8)×(-5)
= -4-48+40
= -12
hence, v.w= -12
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