Question

Please help!!

Use the given vectors to find the indicated quantities.
u =(5, - 2), v =(0, 1), w =(-1, -3)
(a) (u • v)w (b) 5u • V

Answer 1

Part (a)

Lets say we had the two general vectors

u = (a,b)

v = (c,d)

The dot product is

u dot v = a*c + b*d

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Apply that rule to these specific vectors

u = (5, -2)

v = (0, 1)

So we get

u dot v = 5*0 + (-2)*1

u dot v = 0 - 2

u dot v = -2

Therefore,

(u dot v)*w = -2*(-1, -3)

(u dot v)*w = ( -2*(-1), -2(-3) )

(u dot v)*w = (2, 6)

Answer:  (2, 6)

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Part (b)

u = (5, -2)

5u = 5*(5, -2)

5u = (5*5, 5*(-2))

5u = (25, -10)

5u dot v = (25, -10) dot (0,1)

5u dot v = 25*0 + (-10)*1

5u dot v = 0 - 10

5u dot v = -10

Answer: -10