Vector Operations and Properties

Linear combinations of unit vectors p, q, and r

Linear combinations of unit vectors x, y, and z

Linear combinations of unit vectors i, j, and k

Linear combinations of unit vectors a, b, and c

Negative 4

Positive 1

Positive 3

Positive 2

Positive 10

Negative 12

Negative 10

Positive 12

5i - 2j - 9k

5i + 2j + 9k

5i + 2j - 9k

5i - 2j + 9k

As an addition problem

As a division problem

As a multiplication problem

As a subtraction problem

Blue

Red

Green

Purple

Opposite to vector b

Same as vector b

Perpendicular to vector b

Parallel to vector b

Same magnitude

Three times the magnitude

Twice the magnitude

Half the magnitude

A vector with the initial point at the origin

A vector with the terminal point at the origin

A vector in the opposite direction of vector a

A vector in the opposite direction of vector b

Calculating vector magnitudes

Showing vectors in 3D

Showing vectors in 2D

Finding vector directions