Ch. 7 - Applications of Trigonometry and Vectors

Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo

Lial 12th Edition

Ch. 7 - Applications of Trigonometry and Vectors

Problema 41a

Capitolo 8, Problema 41a

Given vectors u and v, find: 2u.
u = 2i, v = i + j

Guida verificata passo dopo passo

Identify the given vector \( \mathbf{u} \). Here, \( \mathbf{u} = 2\mathbf{i} \), which means the vector has a component of 2 in the \( \mathbf{i} \) (x) direction and 0 in the \( \mathbf{j} \) (y) direction.

Understand that multiplying a vector by a scalar (in this case, 2) means multiplying each component of the vector by that scalar.

Write the scalar multiplication operation: \( 2\mathbf{u} = 2 \times (2\mathbf{i}) \).

Multiply the scalar 2 by each component of \( \mathbf{u} \). Since \( \mathbf{u} = 2\mathbf{i} + 0\mathbf{j} \), this becomes \( 2 \times 2\mathbf{i} + 2 \times 0\mathbf{j} \).

Simplify the expression to get the resulting vector \( 2\mathbf{u} \).

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Vector Representation in Component Form

Vectors can be expressed as a combination of unit vectors along coordinate axes, such as i and j in two dimensions. For example, u = 2i means the vector has a magnitude of 2 units along the x-axis and zero along the y-axis.

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Percorso guidato

03:55

Position Vectors & Component Form

Scalar Multiplication of Vectors

Multiplying a vector by a scalar involves multiplying each component of the vector by that scalar. This operation changes the vector's magnitude but not its direction unless the scalar is negative, which reverses the direction.

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Percorso guidato

05:05

Multiplying Vectors By Scalars

Vector Addition and Subtraction

Vectors can be added or subtracted by combining their corresponding components. Although not directly required here, understanding vector addition helps in comprehending vector operations and their geometric interpretations.

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Percorso guidato

05:29

Adding Vectors Geometrically

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