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Suppose that $ a $ and $ b $ are nonzero vectors.(a) Under what circumstances is $ comp_a b = comp_b a $?(b) Under what circumstances is $ proj_a b = proj_b a $?
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Calculus 3
Chapter 12
Vectors and the Geometry of Space
Section 3
The Dot Product
Vectors
Missouri State University
Baylor University
University of Nottingham
Idaho State University
Lectures
02:56
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.
11:08
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.
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The problem is suppose that a and b are not 0 vectors at a and worth sesame. Dense is the scattered projection of b unto a is equal to the scattered projection of a into b. So, for part, a as a definition, we half the scalar projection of b into a is equal to a dot b over minute of a and scale projection of a on to b is equal to b dot a over b. So if a dot b is equal to 0 or the magnet of a is equal to the magnitude of b, then the scale projection of b unto a is equal to scale, projection of a onto b and the work. And the word circumstances is projection of b. Unto a is equal to the water projection of a anton. By definition, the work to projection of b onto a is equal to a dot b over the magnitude of a square times a and this fracture projection of a and b is equal to b dot. A over magnitude of v square times b to be half if the dot product a dot b is equal to 0 or a over. The magnitude of a square is equal to p. Over the magnitude of v square, then work projection of b, a a is equal to the work to projection of a and b.
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