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

2:50 minutes

Problem 35

Textbook Question

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

Verified step by step guidance

First, understand that the notation \(||2u||\) represents the magnitude of the vector \(2u\).

Calculate the vector \(2u\) by multiplying each component of \(u = 2i - 5j\) by 2, resulting in \(2u = 4i - 10j\).

To find the magnitude of \(2u\), use the formula for the magnitude of a vector \(a\mathbf{i} + b\mathbf{j}\), which is \(\sqrt{a^2 + b^2}\).

Substitute the components of \(2u\) into the formula: \(a = 4\) and \(b = -10\), giving \(\sqrt{4^2 + (-10)^2}\).

Simplify the expression under the square root to find the magnitude of \(2u\).

Verified video answer for a similar problem:

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

Video duration:

Play a video:

Was this helpful?

Key Concepts

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

Vector Magnitude

The magnitude of a vector is a measure of its length and is calculated using the formula ||v|| = √(x² + y²) for a vector v = xi + yj in two dimensions. This concept is essential for understanding how to scale vectors and compute their lengths, which is necessary for the given problem.

Scalar Multiplication of Vectors

Scalar multiplication involves multiplying a vector by a scalar (a real number), which scales the vector's magnitude without changing its direction. For example, if u is a vector and k is a scalar, then ku results in a vector that is k times longer or shorter than u, depending on the value of k.

Vector Notation and Operations

Vector notation uses components to represent vectors in a coordinate system, such as u = 2i - 5j. Understanding how to manipulate these components through addition, subtraction, and scalar multiplication is crucial for solving vector-related problems, including finding ||2u||.