In the context of motion in a plane, vectors are often used to represent physical quantities such as displacement, velocity, and acceleration. These vectors can be multiplied by real numbers, which is known as scalar multiplication.
When a vector is multiplied by a positive real number, its magnitude is scaled up by that factor. For example, if a displacement vector of magnitude 5 meters is multiplied by a scalar of 2, the resulting vector will have a magnitude of 10 meters.
When a vector is multiplied by a negative real number, its direction is reversed and its magnitude is scaled up by the absolute value of that factor. For example, if a velocity vector of magnitude 10 meters per second is multiplied by a scalar of -3, the resulting vector will have a magnitude of 30 meters per second in the opposite direction.
Scalar multiplication can be used to represent stretching or compressing a vector, as well as reversing its direction. In the context of motion in a plane, scalar multiplication can be used to represent changes in the speed or direction of an object.
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