Question

Refer to vectors a through h below. Make a copy or a sketch of each vector, and then draw a sketch to represent each of the following. For example, find a + e by placing a and e so that their initial points coincide. Then use the parallelogram rule to find the resultant, as shown in the figure on the right.

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c + d

Accepted Answer

Begin by sketching vectors $$ \mathbf{c} $$ and $$ \mathbf{d} $$ separately, ensuring you represent their directions and magnitudes accurately based on the given information or image. Place the initial point of vector $$ \mathbf{d}  at $$the terminal point of vector $$ \mathbf{c}  to $$prepare for vector addition using the head-to-tail method. Draw the resultant vector $$ \mathbf{c} + \mathbf{d} $$ starting from the initial point of $$ \mathbf{c}  to $$the terminal point of $$ \mathbf{d} $$ after it has been moved. Alternatively, use the parallelogram rule by placing both vectors $$ \mathbf{c} $$ and $$ \mathbf{d} $$ with their initial points coinciding, then complete the parallelogram and draw the diagonal from the common initial point to find the resultant vector. Label the resultant vector clearly on your sketch to represent $$ \mathbf{c} + \mathbf{d} $$, and verify the direction and magnitude visually or by calculation if coordinates or components are available.

Key Concepts

Vector Addition

Parallelogram Rule

Vector Representation and Sketching