https://file.aiquickdraw.com/mathbot/file/1726098614518sy7znayh.jpg

From the image, we see two vectors: **\(\vec{u}\)** and **\(\vec{v}\)**. The question asks by what scalar multiple vector **\(\vec{u}\)** has been scaled to produce vector **\(\vec{v}\)**.

Key observations:
1. **Length change**: It seems that **\(\vec{v}\)** is approximately twice the length of **\(\vec{u}\)**, but in the opposite direction.
2. **Direction**: Since **\(\vec{v}\)** points in the opposite direction to **\(\vec{u}\)**, the scalar must be negative.

Therefore, the scalar that **\(\vec{u}\)** has been multiplied by to obtain **\(\vec{v}\)** is approximately **\(-2\)**.

The correct answer is **\(-2\)**.

Would you like further clarification? Here are 5 questions to expand on this topic:

1. How do scalar multiplications affect the direction of vectors?
2. What is the geometric significance of a negative scalar in vector multiplication?
3. How can you calculate the magnitude of a vector after a scalar multiplication?
4. Can scalar multiplication change a vector's magnitude without affecting its direction?
5. What is the relationship between scalar products and vector dot products?

**Tip**: When a vector's direction changes, check if the scalar is negative.

By what approximate scalar amount has vector \(\vec{u}\) been multiplied by to produce vector \(\vec{v}\)?

Understand how to determine the scalar by which vector \(\vec{u}\) has been multiplied to produce vector \(\vec{v}\). This problem involves key vector multiplication concepts, direction changes, and understanding scalar values. Ideal for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation