Vector Projection Important Terms
To find the vector projection we need to learn to find the angle between two vectors and also to calculate the dot product between two vectors.
Angle Between Two Vectors
The angle between the two vectors is given as the inverse of the cosine of the dot product of two vectors divided by the product of the magnitude of two vectors.
Let’s say we have two vectors [Tex]\vec A[/Tex] and [Tex]\vec B[/Tex] angle between them is θ
⇒ cos θ = [Tex]\frac{\vec A.\vec B}{|A|.|B|} [/Tex]
⇒ θ = cos-1[Tex]\frac{\vec A.\vec B}{|A|.|B|} [/Tex]
Dot Product of Two Vectors
Let’s say we have two vectors [Tex]\vec A[/Tex] and [Tex]\vec B[/Tex] defined as [Tex]\vec A = a_1\hat i + a_2\hat j + a_3\hat k[/Tex] and [Tex]\vec B = b_1\hat i + b_2\hat j + b_3\hat k [/Tex] then dot product between them is given as
[Tex]\vec A.\vec B = (a_1\hat i + a_2\hat j + a_3\hat k)(b_1\hat i + b_2\hat j + b_3\hat k) [/Tex]
⇒ [Tex]\vec A.\vec B[/Tex]= a1b1 + a2b2 +a3b3
Related Article:
Vector Projection – Formula, Derivation & Examples
Vector Projection is the shadow of a vector over another vector. The projection vector is obtained by multiplying the vector with the Cos of the angle between the two vectors. A vector has both magnitude and direction. Two vectors are said to be equal if they have the same magnitude as well as the direction. Vector Projection is essential in solving numerical in physics and mathematics.
In this article, we will learn about what is vector projection, the vector projection formula example, the vector projection formula, vector projection formula derivation, vector projection formula linear algebra, vector projection formula 3d, and some other related concepts in detail.
Table of Content
- What is Vector Projection?
- Vector Projection Formula
- Vector Projection Formula Derivation
- Vector Projection Formula Examples
- Practical Applications and Significance of Vector Projection
- Real-World Problem-Solving Examples of Vector Projection