Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

8. Vectors

Geometric Vectors

Trigonometry

8. Vectors

Geometric Vectors

Previous problemNext problem

Problem 7.41c

Textbook Question

Given vectors u and v, find: v - 3u.
u = 2i, v = i + j

Verified step by step guidance

Identify the given vectors: \( \mathbf{u} = 2\mathbf{i} \) and \( \mathbf{v} = \mathbf{i} + \mathbf{j} \).

Multiply vector \( \mathbf{u} \) by 3: \( 3\mathbf{u} = 3(2\mathbf{i}) = 6\mathbf{i} \).

Subtract \( 3\mathbf{u} \) from \( \mathbf{v} \): \( \mathbf{v} - 3\mathbf{u} = (\mathbf{i} + \mathbf{j}) - 6\mathbf{i} \).

Combine like terms: \( (\mathbf{i} - 6\mathbf{i}) + \mathbf{j} = -5\mathbf{i} + \mathbf{j} \).

The resulting vector is \( -5\mathbf{i} + \mathbf{j} \).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Play a video:

Was this helpful?

Key Concepts

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

Vector Operations

Vector operations involve mathematical manipulations of vectors, such as addition, subtraction, and scalar multiplication. In this case, we are tasked with subtracting a scaled version of vector u from vector v. Understanding how to perform these operations is essential for solving vector-related problems.

Scalar Multiplication

Scalar multiplication refers to the process of multiplying a vector by a scalar (a real number), which scales the vector's magnitude without changing its direction. For example, multiplying vector u by 3 in the expression 'v - 3u' means each component of u is multiplied by 3, affecting the resultant vector's position in space.

Vector Representation

Vectors are often represented in component form, such as u = 2i and v = i + j, where 'i' and 'j' are unit vectors in the x and y directions, respectively. Understanding how to interpret and manipulate these representations is crucial for performing vector calculations accurately.

Watch next

Master Introduction to Vectors with a bite sized video explanation from Patrick

Start learning

Related Videos

Related Practice

Textbook Question

CONCEPT PREVIEW Refer to vectors a through h below. Make a copy or a sketch of each vector, and then draw a sketch to represent each of the following. For example, find a + e by placing a and e so that their initial points coincide. Then use the parallelogram rule to find the resultant, as shown in the figure on the right.

<IMAGE>

-b

375

views

Textbook Question

Find the dot product for each pair of vectors.

4i, 5i - 9j

543

views