Physics: Vectors and Scalars

A physical quantity described by a single number and a unit, without a direction.

A physical quantity that has both magnitude (size) and direction.

Speed in a specific direction.

Change in position of an object, a vector quantity.

A system used to describe locations in two dimensions using perpendicular axes.

The point where the perpendicular axes intersect in a Cartesian coordinate system.

The size or extent of something.

Describing locations using two axes.

A coordinate system that represents a point using a distance from a reference point and an angle from a reference direction.

A coordinate system that represents a point using distances along perpendicular axes.

Place the tail of one vector at the tip of another. The resultant vector starts at the tail of the first and ends at the tip of the second.

To add multiple vectors, draw them head-to-tail. The resultant vector goes from the tail of the first to the head of the last.

The order in which vectors are added does not change the resultant vector.

The vector that results from adding two or more vectors.

A method for adding vectors by placing the tail of one vector at the head of another.

When adding three or more vectors, the sum is the same regardless of how the vectors are grouped.

Adding vectors with the same units and type.

A vector with the same magnitude but opposite direction.

Adding the negative of one vector to another.

Multiplying or dividing a vector by a number to scale its magnitude, keeping the direction the same, if positive scalar

A quantity with only magnitude, no direction.

Vectors must use consistent units (e.g., all velocities in km/hr, or all displacements in meters).

Motion of an object along a straight line, changing its position from one point to another.

Motion of an object around a fixed axis, like a spinning top or the Earth around its axis.

Back-and-forth motion of an object about a fixed point, like a pendulum swinging.

Describing a moving object as a point-like object, ignoring its size and internal structure.

A fixed position used as a starting point to describe the location of an object.

The location of an object relative to a chosen reference point.

A system used to describe locations in space by using numbers or coordinates.

The change in position of the hiker on the first day, represented as a vector with magnitude and direction. The hiker walks 25.0 km southeast.

The change in position of the hiker on the second day, represented as a vector with magnitude and direction. The hiker walks 40.0 km in a direction 60.0° north of east.

The overall change in position of the hiker from the starting point to the final destination, represented as a vector.

These are the projections of a displacement vector onto the x-axis and y-axis, representing the horizontal and vertical changes in position.

Vectors with a magnitude of 1 that point in the direction of the x-axis and y-axis, respectively. They are used to represent directions.

Displacement is the change in position, a vector quantity. Distance is the total length of the path traveled, a scalar quantity.

Yes, force is a vector quantity. It has both magnitude and direction.

No, the height of a building is a scalar quantity. It has only magnitude, no direction.

A vector can be broken down into perpendicular parts called components. These components represent the vector's influence in each direction.

The lengths of a vector's components are found using trigonometry. The hypotenuse of the right triangle is the vector's magnitude, and the components are the adjacent and opposite sides.

The signs of the components (positive or negative) depend on the quadrant where the vector lies. For example, a vector in the second quadrant has a negative x-component and a positive y-component.

A vector with a magnitude of 1, used to represent a direction. The common unit vectors are i (x-direction), j (y-direction), and k (z-direction).

A vector can be expressed using unit vectors and its components. For example, a vector A in the xy plane is written as A = Axi + Ayj.

A vector that represents a portion of a larger vector's influence in a specific direction. It is parallel to a coordinate axis and has a magnitude equal to the corresponding component of the original vector.

A convenient way to represent a vector in the x-y plane using unit vectors i and j for the x and y directions respectively. This simplifies the representation to a linear combination of the components multiplied by the corresponding unit vectors.