Scalar Multiplication of Vectors Flashcards

A quantity with both magnitude and direction.

A quantity with only magnitude, not direction.

The process of multiplying a vector by a scalar, which changes the magnitude of the vector but not its direction (unless the scalar is negative).

The vector's magnitude increases or decreases, but its direction remains the same.

The vector's magnitude changes, and its direction is reversed.

Multiplying a vector by 0 results in the zero vector, which has no magnitude or direction.

If k is a scalar and v is a vector, scalar multiplication is written as k * v.

If vector v = (2, 3) and scalar k = 3, then k * v = (6, 9).

A unit vector remains a unit vector when multiplied by ±1, but its magnitude changes with other scalars.

Scalar multiplication stretches or compresses a vector along its line of action, and reverses its direction if the scalar is negative.