https://file.aiquickdraw.com/mathbot/file/17265832868354tsidccp.jpg

The problem asks for the value of \( \| c\mathbf{u} \| \), where \( \mathbf{u} = \langle 5, -12 \rangle \) and \( c = -3 \).

### Solution:
First, \( c\mathbf{u} \) represents the scalar multiplication of vector \( \mathbf{u} \) by the constant \( c \). So,

\[
c\mathbf{u} = -3 \times \langle 5, -12 \rangle = \langle -15, 36 \rangle
\]

Now, we need to find the magnitude (norm) of this new vector \( \langle -15, 36 \rangle \). The magnitude of a vector \( \mathbf{v} = \langle v_1, v_2 \rangle \) is given by:

\[
\| \mathbf{v} \| = \sqrt{v_1^2 + v_2^2}
\]

So,

\[
\| c\mathbf{u} \| = \sqrt{(-15)^2 + 36^2} = \sqrt{225 + 1296} = \sqrt{1521} = 39
\]

Thus, \( \| c\mathbf{u} \| = 39 \).

The correct answer is **39**.

Do you want more details on this calculation, or have any other questions?

Here are five related questions to further your understanding:
1. What is the general formula for the magnitude of a vector?
2. How does scalar multiplication affect the magnitude of a vector?
3. How would the problem change if \( c = 2 \)?
4. What happens to the direction of a vector when multiplied by a negative scalar?
5. Can the magnitude of a vector ever be negative?

**Tip**: When multiplying a vector by a scalar, remember that the magnitude scales by the absolute value of the scalar, but the direction reverses if the scalar is negative.

Let **u** = ⟨5, −12⟩ and **c** = −3. What is ||cu||?

Learn how to find the magnitude of the vector ⟨5, −12⟩ scaled by the constant −3. This example uses vector operations, including scalar multiplication and magnitude calculation, suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation