Vectors

Vectors, in mathematical terms, are entities that possess both direction and magnitude (size). This differentiates them from scalars, which only contain magnitude. In the field of physics, vectors are employed to illustrate quantities such as force and velocity. In the realm of computer science, they are utilized for spatial representations and algorithms. Operations such as addition, subtraction, and multiplication by scalars can be performed on vectors.

Vector Addition

Given vectors \(\vec{A} = [2, 3]\) and \(\vec{B} = [4, -1]\). Find the result of the vector addition \(\vec{A} + \vec{B}\).

Vector Subtraction

Given vectors \(\vec{A} = 3\hat{i} + 2\hat{j} - 4\hat{k}\) and \(\vec{B} = -2\hat{i} + 3\hat{j} + 5\hat{k}\), find the vector \(\vec{A} - \vec{B}\).

Vector Multiplication by a Scalar

Let vector \( \mathbf{v} = \begin{bmatrix} 2 \ \ 3 \ \ 4 \end{bmatrix} \). What is the result of scalar multiplication of vector \( \mathbf{v} \) by scalar \( 5 \)?

Finding the Position Vector

If a particle moves from the origin O(0,0,0) to the point A(4,5,6), what is the position vector of A?