Vectors

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Vectors "v" and "w" are given by v = 5i - 2j and w = i + 3j. Find scalars r and s such that r ( v - w) = ( r + s )i - 20j.

• Vectors -

r(v-w)=(r+s)i-20j

r(v-w) dot i=r+s

(5ri-2rj-ri-3rj)dot i= r+s
5r-r=r+s
4r=s

Now the j components
r(v-w)dot j=-20
-2r-3r=-20
r=4 then s=1

• Vectors -

WAT DO U MEAN BY DOT?

• Correction - Vectors -

The answer given above is incorrrect

let v = [5,-2) and w = [1,3]
then v-w = [4,-5]

so we want r[4,-5] = [r+s, -20]
then 4r = r+s and -5r = -20
3r = s and r = 4

then r = 4, then s = 12

verification:
LS = r(v-w)
= 4[4,-5] = [16, -20]
RS = [r+s, -20 = 16, -20 ] = LS

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