Skip to main content
Ch. 4 - Laws of Sines and Cosines; Vectors
Blitzer - Trigonometry 3rd Edition
Blitzer3rd EditionTrigonometryISBN: 9780137316601Not the one you use?Change textbook
All textbooksBlitzer 3rd EditionCh. 4 - Laws of Sines and Cosines; VectorsProblem 28
Chapter 4, Problem 28

In Exercises 27–30, let v = i - 5j and w = -2i + 7j. Find each specified vector or scalar.
w - v

Verified step by step guidance
1
Identify the given vectors: \( \mathbf{v} = \mathbf{i} - 5\mathbf{j} \) and \( \mathbf{w} = -2\mathbf{i} + 7\mathbf{j} \).
Recall that vector subtraction \( \mathbf{w} - \mathbf{v} \) means subtracting the corresponding components of \( \mathbf{v} \) from \( \mathbf{w} \).
Write the subtraction component-wise: \( (w_x - v_x)\mathbf{i} + (w_y - v_y)\mathbf{j} \), where \( w_x \) and \( w_y \) are the components of \( \mathbf{w} \), and \( v_x \) and \( v_y \) are the components of \( \mathbf{v} \).
Substitute the components: \( (-2 - 1)\mathbf{i} + (7 - (-5))\mathbf{j} \).
Simplify the expressions inside the parentheses to find the resulting vector components.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
3m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Vector Representation in Component Form

Vectors can be expressed in terms of their components along the standard unit vectors i and j, representing the x and y directions respectively. For example, v = i - 5j means the vector has components (1, -5). This form allows for straightforward algebraic operations on vectors.
Recommended video:
03:55
Position Vectors & Component Form

Vector Subtraction

Vector subtraction involves subtracting corresponding components of two vectors. Given vectors v = (v_x, v_y) and w = (w_x, w_y), the difference w - v is (w_x - v_x, w_y - v_y). This operation results in a new vector representing the displacement from v to w.
Recommended video:
05:29
Adding Vectors Geometrically

Geometric Interpretation of Vector Operations

Vector subtraction can be visualized as finding the vector pointing from the tip of v to the tip of w. This helps in understanding relative positions and directions in the plane, which is essential in physics and engineering contexts.
Recommended video:
05:29
Adding Vectors Geometrically
Related Practice
Textbook Question

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

v = 3i, w = -4i

1
views
Textbook Question

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

a = 14 meters, b = 12 meters, c = 4 meters

Textbook Question

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

5v

1
views
Textbook Question

In Exercises 23–32, use the dot product to determine whether v and w are orthogonal. v = 2i - 2j, w = -i + j

Textbook Question

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

a = 11 yards, b = 9 yards, c = 7 yards

Textbook Question

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 = 7, b = 28, A = 12°

1
views