Question

On a piece of graph paper, draw arrows representing the following vectors. Make sure the tip and tail of each arrow you draw are clearly distinguishable. (a) Placing the tail of the vector at $⟨\mathbf{5}\mathbf{,}\mathbf{2}\mathbf{,}\mathbf{0}⟩$, draw an arrow representing the vector$\overrightarrow{\mathrm{p}}=⟨\mathbf{-}\mathbf{7}\mathbf{,}\mathbf{3}\mathbf{,}\mathbf{0}⟩$ Label it$\overrightarrow{\mathbf{p}}$ . (b) Placing the tail of the vector at$⟨\mathbf{-}\mathbf{5}\mathbf{,}\mathbf{8}\mathbf{,}\mathbf{0}⟩$ , draw an arrow representing the vector$-\overrightarrow{\mathrm{p}}$ . Label it $\mathbf{-}\overrightarrow{\mathbf{p}}$.

Short answer

a.

b.

Step-by-step solution

Drawing vector p→

(a) A vector is an element of a vector space. For many specific vector spaces, the vectors have received specific names, which are listed below. In general, a Euclidean vector is a geometric object with both length and direction.

Draw this vector (i.e.$⟨-7,3,0⟩$ ) as follow, Start from the location $⟨5,2,0⟩$, shift in the $-\mathrm{x}$-direction by 7 units, then shift in the $+y$-direction by 3 units, and remain in the$x,y$ -plane since the$\mathrm{z}$ components are zero.

Drawing vector −p→

b.

Notice that the vector $-\overrightarrow{\mathrm{p}}$has the same magnitude but points in exactly the opposite direction as the vector $\overrightarrow{\mathrm{p}}$.