10.8 Vectors  (Page 7/22)

What are the characteristics of the letters that are commonly used to represent vectors?

How is a vector more specific than a line segment?

What are $i$ and $j,$ and what do they represent?

What is component form?

When a unit vector is expressed as $⟨a,b⟩,$ which letter is the coefficient of the $i$ and which the $j?$

Given a vector with initial point $\left(5,2\right)$ and terminal point $\left(-1,-3\right),$ find an equivalent vector whose initial point is $\left(0,0\right).$ Write the vector in component form $⟨a,b⟩.$

Given a vector with initial point $\left(-4,2\right)$ and terminal point $\left(3,-3\right),$ find an equivalent vector whose initial point is $\left(0,0\right).$ Write the vector in component form $⟨a,b⟩.$

Given a vector with initial point $\left(7,-1\right)$ and terminal point $\left(-1,-7\right),$ find an equivalent vector whose initial point is $\left(0,0\right).$ Write the vector in component form $⟨a,b⟩.$

$P_1=\left(5,1\right),P_2=\left(3,-2\right),P_3=\left(-1,3\right),$ and $P_4=\left(9,-4\right)$

$P_1=\left(2,-3\right),P_2=\left(5,1\right),P_3=\left(6,-1\right),$ and $P_4=\left(9,3\right)$

$P_1=\left(-1,-1\right),P_2=\left(-4,5\right),P_3=\left(-10,6\right),$ and $P_4=\left(-13,12\right)$

$P_1=\left(3,7\right),P_2=\left(2,1\right),P_3=\left(1,2\right),$ and $P_4=\left(-1,-4\right)$

$P_1=\left(8,3\right),P_2=\left(6,5\right),P_3=\left(11,8\right),$ and $P_4=\left(9,10\right)$

Given initial point $P_1=\left(-3,1\right)$ and terminal point $P_2=\left(5,2\right),$ write the vector $v$ in terms of $i$ and $j.$

Given initial point $P_1=\left(6,0\right)$ and terminal point $P_2=\left(-1,-3\right),$ write the vector $v$ in terms of $i$ and $j.$

Find u + ( v − w )

Find 4 v + 2 u

$u=⟨2,-3⟩,v=⟨1,5⟩$

$u=⟨-3,4⟩,v=⟨-2,1⟩$

Let v = −4 i + 3 j . Find a vector that is half the length and points in the same direction as $v.$

Let v = 5 i + 2 j . Find a vector that is twice the length and points in the opposite direction as $v.$

a = 3 i + 4 j

b = −2 i + 5 j

c = 10 i – j

$d=-\frac{1}{3}i+\frac{5}{2}j$

u = 100 i + 200 j

u = −14 i + 2 j

$⟨0,4⟩$

$⟨6,5⟩$

$⟨2,\mathrm{-5}⟩$

$⟨\mathrm{-4},\mathrm{-6}⟩$

Given u = 3 i − 4 j and v = −2 i + 3 j , calculate $u\cdot v.$

Given u = − i − j and v = i + 5 j , calculate $u\cdot v.$

Given $u=⟨-2,4⟩$ and $v=⟨-3,1⟩,$ calculate $u\cdot v.$

Given u $=⟨-1,6⟩$ and v $=⟨6,-1⟩,$ calculate $u\cdot v.$

$⟨2,\mathrm{-1}⟩$

$⟨\mathrm{-1},4⟩$

$⟨\mathrm{-3},\mathrm{-2}⟩$