2.1 Vectors in the plane  (Page 8/29)

$\overrightarrow{PQ}$

$\overrightarrow{PR}$

$\overrightarrow{QP}$

$\overrightarrow{RP}$

$\overrightarrow{PQ}+\overrightarrow{PR}$

$\overrightarrow{PQ}-\overrightarrow{PR}$

$2\overrightarrow{PQ}-2\overrightarrow{PR}$

$2\overrightarrow{PQ}+\frac{1}{2}\overrightarrow{PR}$

The unit vector in the direction of $\overrightarrow{PQ}$

The unit vector in the direction of $\overrightarrow{PR}$

A vector $\text{v}$ has initial point $\left(\mathrm{-1},\mathrm{-3}\right)$ and terminal point $\left(2,1\right).$ Find the unit vector in the direction of $\text{v}.$ Express the answer in component form.

A vector $\text{v}$ has initial point $\left(\mathrm{-2},5\right)$ and terminal point $\left(3,\mathrm{-1}\right).$ Find the unit vector in the direction of $\text{v}.$ Express the answer in component form.

The vector $\text{v}$ has initial point $P(1,0)$ and terminal point $Q$ that is on the y -axis and above the initial point. Find the coordinates of terminal point $Q$ such that the magnitude of the vector $\text{v}$ is $\sqrt{5}.$

The vector $\text{v}$ has initial point $P(1,1)$ and terminal point $Q$ that is on the x -axis and left of the initial point. Find the coordinates of terminal point $Q$ such that the magnitude of the vector $\text{v}$ is $\sqrt{10}.$

$\mathbf{\text{a}}=2\mathbf{\text{i}}+\mathbf{\text{j}},$ $\mathbf{\text{b}}=\mathbf{\text{i}}+3\mathbf{\text{j}}$

$\mathbf{\text{a}}=2\mathbf{\text{i}},$ $\mathbf{\text{b}}=\mathrm{-2}\mathbf{\text{i}}+2\mathbf{\text{j}}$

Let $\mathbf{\text{a}}$ be a standard-position vector with terminal point $\left(\mathrm{-2},\mathrm{-4}\right).$ Let $\mathbf{\text{b}}$ be a vector with initial point $\left(1,2\right)$ and terminal point $\left(\mathrm{-1},4\right).$ Find the magnitude of vector $\mathrm{-3}\mathbf{\text{a}}+\mathbf{\text{b}}-4\mathbf{\text{i}}+\mathbf{\text{j}}.$

Let $\mathbf{\text{a}}$ be a standard-position vector with terminal point at $\left(2,5\right).$ Let $\mathbf{\text{b}}$ be a vector with initial point $\left(\mathrm{-1},3\right)$ and terminal point $\left(1,0\right).$ Find the magnitude of vector $\mathbf{\text{a}}-3\mathbf{\text{b}}+14\mathbf{\text{i}}-14\mathbf{\text{j}}.$