Precalculus: Vectors, vector component form, Vector Practice--Dot Product and Addition

<7, 4>

Find component form with initial point (-3,1) terminal point (4,5).

<-7, -4>

Find component form with initial point (4,5) terminal point (-3,1).

53°

Find the direction of <3,4>

37°

Find the direction of <4,3>

2√5

Find the magnitude. <4, 2>

13

Find the magnitude. <5, 12>

-16

Find u · v if u = -3i + j and v = 5i - j.

8

Find u · v if u = ⟨4,0⟩ and v = ⟨2,1⟩.

⟨-6, 10⟩

If u= ⟨0, 8⟩ and v = ⟨-3, 1⟩, find u + 2v.

⟨17, 15⟩

If u= ⟨20, 1⟩ and v = ⟨-3, 14⟩, find u + v.

⟨7, -6⟩

If u= ⟨5, -1⟩ and v = ⟨3, 4⟩, find 2u - v.

orthogonal

Parallel, orthogonal or neither? u=<-2, 1> and v=<5, 10>

neither

Parallel, orthogonal or neither? u=<-2, 2/3> and v=<5, -15>

parallel

Parallel, orthogonal or neither? u=<-2, 2> and v=<5, -5>

3√3(cos3π/4 + isin3π/4)

Trig form of -3 + 3i

4(cos11π/6 + isin11π/6)

Trig form of 2√3 - 2

<-3/5, 4/5>

Unit vector in the same direction as <-3, 4>

<-21/5, 28/5>

Vector in the same direction as <-3,4> with a magnitude of 7

dot product

a=<a₁,a₂> b= <b₁,b₂> a·b= a₁·b₁ + a₂·b₂

horizontal component

a=v·cosθ

vertical component

b=v·sinθ

<3√3, 3>

component form of a vector with magnitude 6 and angle formed with the positive x=axis = 30 degrees

121.5 degrees

find the angle between the given vectors u=3i-2j, v=-4i-2j

147.1 degrees

find the angle between the given vectors u=4i+5j, v=-6i-2j

32.9 degrees

find the angle between the given vectors u=4i-5j, v=6i-2j

5

find the magnitude of the vector u= <3,-4>

vector

has both magnitude and direction

scalar

something described by a single real number.

component form of a vector

start at end, subtract from the beginning: V= (x₂-x₁)i + (y₂-y₁)j

magnitude

√a²+b²