Precalculus: Vectors, vector component form, Vector Practice--Dot Product and Addition
105.945 degrees
FInd the direction angle (θ) for vector v = <-2,7>. Round to three decimals.
<7, 4>
Find component form with initial point (-3,1) terminal point (4,5).
<3, 8>
Find component form with initial point (0, -2) terminal point (3,6).
<3, -8>
Find component form with initial point (3,6) terminal point (0,-2).
<-7, -4>
Find component form with initial point (4,5) terminal point (-3,1).
<85.6, 86.5>
Find the component form of the resultant for the Force vectors given: F1 : magnitude = 60 lbs, θ = 80° F2 : magnitude = 80 lbs, θ = 20°
79°
Find the direction of <1,5>
53°
Find the direction of <3,4>
37°
Find the direction of <4,3>
√61
Find the magnitude <6, 5>
121.66 lbs
Find the magnitude of the resultant for the Force vectors given: F1 : magnitude = 60 lbs, θ = 80° F2 : magnitude = 80 lbs, θ = 20°
5
Find the magnitude. <3,4>
√34
Find the magnitude. <3,5>
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.
-23
Find u · v if u = 2i - 5j and v = 6i + 7j.
73
Find u · v if u = ⟨4, 25⟩ and v = ⟨-13, 5⟩.
8
Find u · v if u = ⟨4,0⟩ and v = ⟨2,1⟩.
56
Find u · v if u = ⟨8, 2⟩ and v = ⟨6, 4⟩.
-8
Find w · v if v = ⟨1,-3⟩ and w = ⟨-2,2⟩.
⟨20, -20⟩
If A(6, 11) and B(-14, 31), find components for vector BA
⟨10, -5⟩
If A(8, -3) and B(18,-8), find components for vector AB.
⟨-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.
⟨9, 8⟩
If u= ⟨20, 6⟩ and v = ⟨-3, 15⟩, find (1/2)u + (1/3)v.
⟨7, -6⟩
If u= ⟨5, -1⟩ and v = ⟨3, 4⟩, find 2u - v.
neither
Parallel, orthogonal or neither? u=<-2, 2/3> and v=<5, -15>
dot product
a=<a₁,a₂> b= <b₁,b₂> a·b= a₁·b₁ + a₂·b₂
horizontal component
a=v·cosθ
vertical component
b=v·sinθ
56.8 degrees
find the angle between the given vectors u=3i+2j, v=-4i-2j
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
8.25
find the magnitude of the vector u= <-2,-8>
5.38
find the magnitude of the vector u= <-2,5>
10.0
find the magnitude of the vector u= <0,10>
5
find the magnitude of the vector u= <3,-4>
7.21
find the magnitude of the vector u=4i-6j
10.63
find the magnitude of the vector u=7i+8j
10.63
find the magnitude of the vector u=7i-8j
vector
has both magnitude and direction
scalar
something described by a single real number.
representing a vector in rectangular coordinates
start at end, subtract from the beginning: V= (x₂-x₁)i + (y₂-y₁)j
magnitude
√a²+b²
