The dot or scalar product of two (3d) vec- tors ⃗a = ⟨a1,a2,a3⟩ and ⃗b = ⟨b1,b2,b3⟩ is defined as
3 ⃗a • ⃗b = a i b i = a 1 b 1 + a 2 b 2 + a 3 b 3 .
i=1
in 3d euclidean space, the scalar product has a geometric interpretation, given by ⃗a • ⃗b = ∥ ⃗a ∥ ∥ ⃗b ∥ c o s θ ,
where θ is the angle between ⃗a and ⃗b and the norm(length) of a vector ∥⃗a∥ is defined by
∥ ⃗a ∥ = √ ⃗a • ⃗a .
in words, the scalar product of two vectors can be thought of as the product of the magnitude of ⃗a with the magnitude of the projection of ⃗b onto the direction of ⃗a. it is used to calculate the product of vector quantities when only the parallel components of each vector contribute (e. g., work = force • displacement).
let ⃗a = ⟨14, 10.5, 0⟩ and ⃗b = ⟨4.62, 9.45, 0⟩. calculate ⃗a • ⃗b.

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i just did this and got a 100.

note: the given question is incomplete.

complete question is given below.

which is an example of kinetic energy?

a. the energy stored in ethanol  

b. a hockey puck sliding across the ice  

c. a compressed spring  

d. a ball sitting at the top of a ramp

solution: the kinetic energy is the energy posses by the virtue of the motion of the object.

in the given options, a, c and d are the example of potential energy because it is the energy posses by the virtue of the rest of the object. but option b has the kinetic energy as the object is in motion.

hence, a hockey puck sliding across the ice   is the apex example of kinetic energy.

so, the option (b) a hockey puck sliding across the ice   is the correct option.