Orthogonal Projections and Vector Analysis

A subtraction of one vector from another

A multiplication of two vectors

A decomposition of a vector into two orthogonal vectors

A vector addition process

A line parallel to vector Y

A line perpendicular to vector V

A line that bisects vector V

A line created by all scalar multiples of vector V

To add two vectors together

To calculate the projection of one vector onto another

To determine the angle between two vectors

To find the length of a vector

By subtracting vector U from vector Y

By using the dot product of Y and U divided by the dot product of U with itself, then multiplying by U

By multiplying the vectors Y and U

By adding the vectors Y and U

Vector 2 1

Vector 0 0

Vector 7 6

Vector 8 4

Dividing the vectors

Multiplying the vectors

Finding the component orthogonal to U

Finding the sum of the vectors

By verifying they are parallel

By confirming their lengths are equal

By ensuring their dot product is zero

By checking if their sum is zero

The vectors are in opposite directions

The vectors are identical

The vectors are orthogonal

The vectors are parallel

Vector 8 4

Vector 7 6

Vector -1 2

Vector 2 1

To determine if they are in the same direction

To confirm the accuracy of the projection

To check if they are equal in magnitude

To ensure they are parallel