Skip to main content
Ch. 4 - Laws of Sines and Cosines; Vectors
Blitzer - Trigonometry 3rd Edition
Blitzer3rd EditionTrigonometryISBN: 9780137316601Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 3rd EditionCh. 4 - Laws of Sines and Cosines; VectorsProblema 25
Capitolo 4, Problema 25

In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar.
v - u

Guida verificata passo dopo passo
1
Identify the given vectors: \( \mathbf{u} = 2\mathbf{i} - 5\mathbf{j} \) and \( \mathbf{v} = -3\mathbf{i} + 7\mathbf{j} \).
Recall that vector subtraction \( \mathbf{v} - \mathbf{u} \) is performed by subtracting the corresponding components of \( \mathbf{u} \) from \( \mathbf{v} \).
Subtract the \( \mathbf{i} \)-components: \( -3 - 2 = -5 \).
Subtract the \( \mathbf{j} \)-components: \( 7 - (-5) = 7 + 5 = 12 \).
Write the resulting vector as \( \mathbf{v} - \mathbf{u} = -5\mathbf{i} + 12\mathbf{j} \).

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
1m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Vector Representation in Component Form

Vectors in two dimensions can be expressed as components along the i (x-axis) and j (y-axis) unit vectors. For example, u = 2i - 5j means the vector has an x-component of 2 and a y-component of -5. Understanding this form allows for straightforward vector operations like addition and subtraction.
Video consigliato:
Percorso guidato
03:55
Position Vectors & Component Form

Vector Subtraction

Vector subtraction involves subtracting corresponding components of two vectors. For vectors v and u, v - u is found by subtracting the x-components and y-components separately, resulting in a new vector. This operation is essential for finding the difference or relative position between vectors.
Video consigliato:
Percorso guidato
05:29
Adding Vectors Geometrically

Unit Vectors i and j

Unit vectors i and j represent the standard basis vectors along the x-axis and y-axis, respectively. They have a magnitude of one and direction along their axes. Expressing vectors in terms of i and j simplifies calculations and visualization in the plane.
Video consigliato:
Percorso guidato
06:01
i & j Notation
Pratica correlata
Domanda del libro di testo

In Exercises 25–26, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j.

P₁ = (-3, 0), P₂ = (-2, -2)

606
views
Domanda del libro di testo
In Exercises 25–26, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j. P₁ = (2, -1), P₂ = (5, -3)
743
views
Domanda del libro di testo

In Exercises 23–32, use the dot product to determine whether v and w are orthogonal.

v = 2i + 8j, w = 4i - j

767
views
Domanda del libro di testo

In Exercises 17–32, two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round to the nearest tenth and the nearest degree for sides and angles, respectively.

a = 10, b = 30, A = 150°

682
views
Domanda del libro di testo

In Exercises 22–24, sketch each vector as a position vector and find its magnitude.

v = -3j

848
views
Domanda del libro di testo

In Exercises 25–30, use Heron's formula to find the area of each triangle. Round to the nearest square unit.

a = 4 feet, b = 4 feet, c = 2 feet

944
views