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Prove Properties 2, 4, and 5 of the dot product (Theorem 2).
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Vectors and the Geometry of Space
The Dot Product
Johns Hopkins University
Missouri State University
Harvey Mudd College
In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.
In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.
Prove Properties $2,4,$ an…
Prove Property 4 of the do…
The problem is proof properties, 24 and 5 of the dot product property 2 is a dot b, is equal to b dot a here we can let a is equal to a 1 a 2. A 3 point b is equal to e o b 2 b 3. So a dot b is equal to a 1 b 1 plus a 2 b 2 plus a 3 b, 3 and b dot a is equal to v, 1, a 1 plus b 2, a 2 plus 8 e 3 a 3. So this is equal to a 1 b 1 plus a 2 v 2 plus 3 b 3 s. This is equal to a dot b. Property 4 is scattered c times. A dot b is equal to scatter c times. A dot b is equal to a dot square c times b, so first to reprove this equation, and similarly we can prove another equation: a is equal to c a 1 c, a 2 c, a 3 point. So c, a dot b is equal to c, a 1 b, 1 plus c, a 2 b, 2 plus c 83 b 3 point. So this is equal to c times a 1 b, 1 plus a 2 b, 2 plus 83 b 3 point. So this is equal to s times a dot b. To similarly become proof. The other equation- property 5- is 0 dot. A is equal to 00 is a vector, 000 point, so 0 dot a is equal to 0 times a 1 plus 0 times a 2 plus 0 times a 3 point. So this is equal to 0.
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