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Find the scalar and vector projections of $ b $ onto $ a $.

$ a = \langle -1, 4, 8 \rangle $ , $ b = \langle 12, 1, 2 \rangle $

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Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 3

The Dot Product

Vectors

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Boston College

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.

Find the scalar and vector…

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For two-dimensional vector…

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$29-32$ Find the scalar an…

The problem is finding the scaler and vector projections of b unto a a is equal to negative 148 b is equal to 1212 point. So first th magnitude of a is equal to root of 1 plus 16 plus 64 point. So this is equal to 9, but we have to scatter projections of b on to a this is equal to a dot b over magnitude. To a point. This is equal to negative 12 plus 4 plus 16 over 9 point. So this is equal to 8. Over 9 point, then, the work projections of b o o a this is equal to scaler projections of b unto a times vector. A overdue of this is equal to 8 over 81 times negative 148 point. This is equal to negative 8 over 8132 over 81 and 64.

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