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

$ a = \langle 4, 7, -4 \rangle $ , $ b = \langle 3, -1, 1 \rangle $

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Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 3

The Dot Product

Vectors

Campbell University

Baylor University

University of Michigan - Ann Arbor

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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Find the vector.$\over…

The problem is find the scaler and the factor. Productions of b into a a is equal to 47 negative 4 b is equal to 3 negative, 1 and 1 point so first, the magnitude of a is equal to but 16 plus 49 plus 16 point. This is equal to 9, then be half the scatter projections of b into a this is equal to a dot b over the magnitude of a so. This is equal to 12 minus 7 minus 4 over 9 point. So this is equal to 1 over 9. Then the projection work, the projections of b into a is equal to 1 over 9 times victor over the magnitude of a point. This is equal to 1 over 81 o times 47 negative 4 point. This is equal to 4 over 817 over 81 and negative 4. Over 8.

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