Dot Product Example

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Dot Product Example

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Calculating work done the dot product in physics

Calculating Work Done The Dot Product In Physics

Example Calculate the dot product of vectors a and b a b a b cos a b 10 13 cos 59 5 a b 10 13 0 5075 a b 65 98 66 rounded OR we can calculate it this way a b a x b x a y b y a b 6 5 8 12 a b Definition: dot product. The dot product of vectors ⇀ u = u1, u2, u3 and ⇀ v = v1, v2, v3 is given by the sum of the products of the components. ⇀ u ⋅ ⇀ v = u1v1 + u2v2 + u3v3. Note that if u and v are two-dimensional vectors, we calculate the dot product in a similar fashion.

Statics example dot product youtube

Statics Example Dot Product YouTube

Dot Product ExampleExample 1: Let there be two vectors [6, 2, -1] and [5, -8, 2]. Find the dot product of the vectors. Solution: Given vectors: [6, 2, -1] and [5, -8, 2] be a and b respectively. a.b = (6)(5) + (2)(-8) + (-1)(2) a.b = 30 – 16 – 2. a.b = 12. Example 2: Let there be two vectors |a|=4 and |b|=2 and θ = 60°. Find their dot product. Solution: a.b . Example 1 Calculate the dot product of a 1 2 3 a 1 2 3 and b 4 5 6 b 4 5 6 Do the vectors form an acute angle right angle or obtuse angle Solution Using the component formula for the dot product of three dimensional vectors a b a1b1 a2b2 a3b3 a b a 1 b 1 a 2 b 2 a 3 b 3