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Dot Product Calculator

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Example
Created on 2024-06-20Asked by Noah Rodriguez (Solvelet student)
Compute the dot product of the vectors u=⟨2,−1,3⟩ \mathbf{u} = \langle 2, -1, 3 \rangle and v=⟨−3,1,2⟩ \mathbf{v} = \langle -3, 1, 2 \rangle .

Solution

The dot product of vectors u \mathbf{u} and v \mathbf{v} is given by: u⋅v=(2)(−3)+(−1)(1)+(3)(2)=−6−1+6=−1. \mathbf{u} \cdot \mathbf{v} = (2)(-3) + (-1)(1) + (3)(2) = -6 - 1 + 6 = -1. Solved on Solvelet with Basic AI Model
Some of the related questions asked by Layla Nguyen on Solvelet
1. Compute the vector dot product u=⟨3,−2,5⟩ \mathbf{u} = \langle 3, -2, 5 \rangle and v=⟨1,4,−2⟩ \mathbf{v} = \langle 1, 4, -2 \rangle .2. Find the angle between the vectors a=⟨2,1,−3⟩ \mathbf{a} = \langle 2, 1, -3 \rangle and b=⟨−1,2,2⟩ \mathbf{b} = \langle -1, 2, 2 \rangle .
DefinitionThe dot product is also known as the inner product or the scalar product and is an algebraic operation that takes two equal-length sequences of numbers and returns a single number. In mathematics, the dot product is the product of the magnitude of two vectors, and the cosine of the angle between them. The dot product is used in geometry, physics and engineering to calculate work, projections, angles and distances between vectors. VS The product of the two vectors and is: a⋅b=a1​b1​+a2​b2​+a3​b3​.\medspace \backsim
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