WorksheetsPrecalculus Application of Vectors
Total questions: 20
Worksheet time: 20mins
a is the position vector of point A
b is the direction vector of line L
r is the position vector of all points in L, represented by P(x,y)
OB + BC = OC
OA + AC = OC
CB + B0 = -OC
OD = 0.5(OA + AC)
Vector a = 2i + 3j - 5k. What is the value of 3a?
3i + 3j - 3k
5i + 6j - 8k
6i + 9j -15k
6i + 6j - 15k
Given parallel vectors u and v. Answer ALL that apply
their scalar product is zero
their scalar product is either 1 or -1
u is a multiple of v
magnitude of u equals the magnitude of v
Find the component form of vector v.
<−6, 3>
<−6, −3>
<6, −3>
<6, 3>
If g = <-1, 1>, y = <1, 1>, z = <-3, -3>, and v = <6, 8>, what is 4g + y + z - 5v?
<24, 42>
<-36, -38>
<36, 38>
<-30, -32>
If a=⟨4,−2⟩ and b=⟨1,2⟩ , what is the dot product a⋅b ?
0
2
6
8
Given an initial point A ( 2, 4 ) and terminal point B ( -8, 7 ), find the component form of the vector AB.
〈-10,3〉
〈-6,3〉
〈10,11〉
〈-6,-3〉
Find the magnitude.
4
5
3
square root of 5
The scalar product of u and v is zero, therefore...
vectors u and v are parallel
vectors u and v are perpendicular
vectors u and v are equal
vectors u and v are multiples
A ferry departs from A(-25, 28). It takes 3 hours to reach its destination B(20, -32), travelling in as straight line with constant velocity. Distances are in km. Find the speed of the ferry.
50 km/h
55 km/h
25 km/h
20 km/h
A ferry departs from A(-25, 28). It takes 3 hours to reach its destination B(20, -32), travelling in as straight line with constant velocity. Distances are in km. Find the velocity vector of the ferry.
15i + 20j
15i - 20j
20i + 15j
20i - 15j
Vector is a quantity with:
magnitude and direction
magnitude
direction
none of the above
Given the vector v = 3i -2j +6 k, the magnitude of a is:
36
49
7
6
Given points A(2, 1) and B(-4, 1). Explain why the vector AB is parallel to the x-axis
because vector AB is a multiple of the unit vector i
because vector AB is a multiple of the unit vector j
because vector AB is a multiple of the unit vector k
A ferry departs from A(-25, 28). It takes 3 hours to reach its destination B(20, -32), travelling in as straight line with constant velocity. Distances are in km. Find the distance that the ferry travels.
50 km
55 km
70 km
75 km
A vector is a mathematical structure that has both _______ and _______.
direction, magnitude
scope, sequence
meat, potatoes
scalar, vector
Which are equivalent vectors?
u and -u
u and a
u and v
u and b
Given an initial point R ( -12, 4 ) and terminal point S ( 28, -17 ), find the component form of the vector RS. Hint: get it into the pointy brackets.
〈14,-13〉
〈-14,13〉
〈-40,-21〉
〈40,-21〉
Given u = <3, 7>, find 2u
<21, 2>
<6, 26>
<6, 14>
23
