Unit Vector: Overview, Questions, Preparation

A unit vector is a vector of a particular direction and unit magnitude. They merely specify the direction. They do not have any unit and dimension. Additionally, it represents direction. It uses a two-dimensional vector since it is simpler to comprehend. A unit vector bears a magnitude of one. 

In the given topic, the unit vector and its formula will be discussed along with its derivation as well as solved problems. 

Additionally, two-dimensional spatial directions depicted like this are parallel numerically to the unit circle’s points. 

Often unit vectors constitute the ground of a vector space. Also, every vector present in space could be shown as a unit vectors’ linear combination. 

Unit vectors are essential in defining the directions of any vector. 

The formula for Unit Vector 

The physical quantities for which both the direction and magnitude are defined separately are called vector quantities. Vectors are denoted by adding an arrow symbol over the letters or other values representing them. 

For instance, to define a motor vehicle’s speed together with its magnitude, its direction must also be mentioned specifically. 

Vectors can be simply denoted by using the coordinate system in three dimensions. 

A vector could be converted into a unit vector by performing division of the vector by the magnitude of the vector. The same can be expressed as follows: - 

Point to be noted, the product of dots of two unit vector is a scalar value amounting to the cosine of the subtended angle, which is smaller, as per Euclidean space. 

Regarding the right-hand rule to determine one of two possible directions, the cross-product equals this differing span, enabling the hinged orthogonal unit vector to both the inputs.

Details of the Topic taught in Class 10

Unit vector means the space of a normal vector that has a length of 1. A lowercase alphabet is used along with the circumflex symbol. The term of direction vector depicts a unit vector to denote the spatial vector. They are denoted as ‘d’. 

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The magnitude can be used to find vector  b 

        

The answers can be left infractions instead of decimal numbers unless required.   

2. If the magnitude between two vectors and their resultant is identical, what is the angle between the two vectors?

Solution.

Given, R=A=B

R=√A² + B² + 2AB cosθ

R²=A²+B²+2AB cosθ

A²=A²+A²+2A²cosθ

cos θ= -½

θ=120°

3.What is a unit vector with the same direction as r = (2, -5)?

Solution

|r| = √2² + √(-5)² = √29

Divide each component of r by |r|

uₓ = (2/√29, - 5/√29)

= (2√29/29, - 5√29/29)

Q: What are the uses of unit vector?

Q: Name any three kinds of vectors?

Q: Explain what a free vector is?

Q: Give an example of a biological vector.

Q: Is position a kind of vector?