Given vectors u and v, find: 2u.
u = 2i, v = i + j

Key Concepts

Vector Representation

Vectors are mathematical objects that have both magnitude and direction, often represented in component form. In this case, vectors u and v are expressed in terms of unit vectors i and j, where i represents the x-direction and j represents the y-direction. Understanding how to interpret and manipulate these components is essential for vector operations.

Scalar Multiplication

Scalar multiplication involves multiplying a vector by a scalar (a real number), which scales the vector's magnitude without changing its direction. For example, multiplying vector u by 2, as in the question, means each component of u is multiplied by 2, resulting in a new vector that is twice as long in the same direction.

Vector Addition and Subtraction

Vector addition and subtraction are performed by adding or subtracting corresponding components of the vectors. While the question specifically asks for scalar multiplication, understanding how to combine vectors is crucial for broader vector operations, as it lays the groundwork for more complex vector manipulations in trigonometry and physics.