Vector Jeopardy

Sum of 2 Vectors

100

Find the sum of the vectors: 

U= <2, -1>

V= <3, 5>

<5, 4>

200

Given Vectors:

U= <2, -1, 3> 

V= <3, 5, 0> 

W= <-2, 0, 3>

α=2 β=-2 γ=4  

FIND: αu+βv+γw

<-10, -12, 18>

300

Given Three Vectors u=⟨2,3,1⟩, v=⟨-2,5,1⟩ and z= u-2v

FIND the magnitude of vector 3z

3 radical 86 

400

The coordinates of the points A,B,C are

A(-1,1,2) B(1,-2,3) C(-2,1,1)

FIND the vector sum of U+V-W if U=AB V=CB W=CA

<4, -6, 2>

500

Find the sum of two vectors (-1,2) to (3,-7)

<4,-9>

Random

100

Find the vector with a given magnitude of 14 and an angle of 120 degrees from the positive x axis.

v = -7i + 7rad 3 j  or -7i + 12.124j

200

Two forces of 30 N and 70 N act on an object at angles of 45 degrees and 120 degrees respectfully with the positive x axis.  Write the equation of the resultant force.

What vector is needed to put this in static equilibrium?

Resultant Force = -13.787 i + 81.835 j

Static Equilibrium:  13.787i - 81.835 j

300

Find the unit vector that is in the same direction as the vector v=[3,6,1]

[4/radical 46, 6/radical 46, 1/radical 46]

400

Put the vector (1,3) in unit vector form.

(1/radical 10, 3/radical 10)

500

What is a vector? 

a directed line segment that depicts the length and direction of arrow (tail to end)

Distance Between Vectors

100

Find the distance (v,w) between the two vectors

v= (1,3) w= (5,2)

radical 17

200

Find the distance between XY if X=⟨1,0,−5⟩ and Y=⟨−3,2,−1⟩

6

300

Compute the distance between the vectors ⟨2,3,5⟩ and ⟨2,0,9⟩

5

400

Find the distance between the vectors ⟨0,1,4⟩ and ⟨2,9,1⟩

radical 77

500

Find the distance between the vectors ⟨1,3,3⟩ and ⟨2,−1,1⟩

radical 21

Dot Product

100

Evaluate the dot product of u=(1,2,3), and v=(9,−2,−10)

-25

200

Find the dot product of the following vectors:

V = <0, 1, -1>

U = <1, 1, 1 >

0

300

Find the dot product of the following vectors:

V = <1, 2, 3>

U = <1, 4, 5>

24

400

Calculate the dot product of c=(−4,−9)c=(−4,−9) and d=(−1,2)d=(−1,2). Do the vectors form an acute angle, right angle, or obtuse angle?

-14 (vectors form an obtuse angle)

500

Calculate the dot product of a=(1,2,3)a=(1,2,3) and b=(4,−5,6)b=(4,−5,6). Do the vectors form an acute angle, right angle, or obtuse angle?

12 (the vectors form an acute angle)

Angle between Vectors

100

Find the angle between these two vectors, u=(3,4), and v=(9,−2)

65.66 degrees

200

Calculate the angle between u=(1,2), v=(3,4)

10.3 degrees

300

Find the approximate acute angle in degrees between the vectors <2,2,5>,<0,5,−1>

80.22

400

Find the angle between the following vectors (to two decimal places):

v=[−2,4,−1],w=[3,1,−5]

1.46

500

Find the angle between vectors u=⟨1,−2,3⟩ and v=⟨−3,−4,−6⟩ and round to the nearest degree

116