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## Introduction to Magnitude of a Vector

**Vectors** are used extensively in mathematics to describe values that have both direction and quantity. The **magnitude of a vector**, often known as its length, gives crucial information about the intensity or size of the quantity it represents. Understanding how to compute and comprehend the magnitude of a vector is critical in physics, engineering, and everyday life.

### What is the definition of magnitude of vector

The magnitude of a **vector reflects** its length or size without taking into account its direction. It’s a scalar quantity represented by |v|, where v represents the vector under consideration.

### Formula for magnitude of a vector

### How to find the magnitude of a vector

- Determine the vector’s components in the given dimension.
- Consider the number of dimensions when calculating the magnitude.
- Square each component, add the squared values, then compute the square root of the sum.

### Solved Examples on Magnitude of Vector

**Example 1:**

Given a vector u = (3, 4) in 2D space, find its magnitude.

**Solution:**|u| = √(3² + 4²) = √(9 + 16) = √25 = 5

**Example 2:**

For a vector w = (1, 2, 3) in 3D space, calculate its magnitude.

**Solution:**|w| = √(1² + 2² + 3²) = √(1 + 4 + 9) = √14

**Also Check:**

## Frequently Asked Questions on Magnitude of a Vector

### What is the significance of magnitude of vector?

Vector magnitude provides information about the intensity or scale of a quantity, regardless of its direction. It's essential for various calculations in physics, engineering, and geometry.

### What is the magnitude of three different unit vectors along the axes?

The magnitude of unit vectors along the axes is always 1. In three-dimensional space, the unit vectors are î for the x-axis, ĵ for the y-axis, and k̂ for the z-axis. The magnitude of î is |î| = 1. The magnitude of ĵ is |ĵ| = 1. The magnitude of k̂ is |k̂| = 1. Unit vectors have a length of 1 and point in the direction of their respective axes. They serve as reference directions in coordinate systems and are used to describe other vectors' components and directions.

### What is the magnitude of a vector in three dimensional space?

The magnitude of a vector in three-dimensional space tells you how long the vector is. Imagine you have a vector that points in three directions: left-right, up-down, and front-back. To find its magnitude, you use the formula √(x² + y² + z²), where x, y, and z are how far the vector goes in each direction. This gives you a single number that represents how big the vector is.

### What is the magnitude of resultant vectors of two vectors?

The magnitude of the resultant vector formed by adding two vectors is calculated using the Pythagorean theorem. In 2D, it's √(Rx² + Ry²), and in 3D, it's √(Rx² + Ry² + Rz²), where Rx, Ry, and Rz are the components of the resultant vector along respective axes.

### If the magnitude of resultant vector of two vectors having magnitudes 5 and 3 is 2 then what is the angle between them?

Angle is 180 degrees

### How does the magnitude of the vector related to unit vector?

Unit vectors have a magnitude of 1 and are used to represent direction. The magnitude of a vector can be understood by the relative scale of its components compared to the unit vectors

### Can the magnitude of the vector is negative?

No, the magnitude of a vector is always a non-negative scalar value.