Draw the given vectors and find their sum graphically. The...

Draw the given vectors and find their sum graphically. The magnitude is shown first, followed by the direction as an angle in standard position.
$$2.3 \mathrm{cm}, 45^{\circ} ; 5.2 \mathrm{cm}, 120^{\circ}$$

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Key Concepts

Direction and Standard Position

The direction of a vector specifies the angle at which the vector is oriented relative to a reference axis, usually the positive x-axis. When an angle is described in standard position, it means the angle is measured counterclockwise from the positive x-axis.

Graphical Vector Addition

Graphical vector addition is a method used to find the resultant vector by placing vectors in a diagram such that their arrangement represents their orientation and magnitude. This approach helps in intuitively understanding how vectors combine their effects.

Vector

A vector is a quantity that has both magnitude and direction. It is typically represented by an arrow, where the length of the arrow corresponds to the magnitude and the direction of the arrow indicates its orientation in space.

Magnitude

Magnitude represents the size or length of a vector. It quantifies how large or small the vector is and is independent of its direction, commonly measured as the distance from the vector's tail to its head.

Tip-to-Tail Method

The tip-to-tail method is a common graphical technique in which the tail of one vector is placed at the tip of the preceding vector. The resultant vector is then drawn from the tail of the first vector to the tip of the final vector, visually representing the sum of the vectors.

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