Free Printable Vectors Assessment

1.

Find $u+v$ given $u=<-10,-4>$ , $v=<-3,8>$

a)

< -14, 4>

b)

< - 7, - 14>

c)

< 7, 4>

d)

< -13, 4>

2.

$v=<6,8>$ Find the magnitude of vector v.

a)

14

b)

100

c)

10

d)

$\sqrt{10}$

3.

Which vector has the same direction as vector v. $v=<-5,-12>$

a)

$<-\frac{13}{5},-\frac{13}{12}>$

b)

$<-\frac{5}{13},-\frac{12}{13}>$

c)

$<\frac{12}{13},\frac{5}{13}>$

d)

$<65,156>$

4.

Find the vector that has the given magnitude and direction angle. $\parallel v\parallel=7,\ \theta=270\degree$

a)

$<0,-7>$

b)

$<-7,0>$

c)

$<-7,-7>$

d)

$<7,7>$

5.

For the given vectors u and v, find the dot product $u\cdot v$
$u=<3.45,6.72>,\ v=<-2.15,5.60>$

a)

45.05

b)

13.62

c)

12.39

d)

30.21

6.

Write the vector with the initial point $\left(-2,4\right)$ and terminal point $\left(-3,5\right)$ in component form.

a)

$<-1,-1>$

b)

$<1,1>$

c)

$<1,-1>$

d)

$<-1,1>$

7.

Evaluate $\parallel<3,-7>\parallel$

a)

$2\sqrt{10}$

b)

$2i\sqrt{10}$

c)

$\sqrt{58}$

d)

$2$

8.

Given vector $v=<-3,7>$ , find the direction angle, θ.

a)

$113.20\degree$

b)

$246.80\degree$

c)

$66.80\degree$

d)

$293.20\degree$

9.

Given $u=<2,-5>,\ v=<-4,1>$ , find $3u+2v$ .

a)

$<-2,-4>$

b)

$<-6,-8>$

c)

$<-2,-13>$

d)

$<10,10>$

10.

Find the resultant of the vectors $<10\cos25\degree,\ 10\sin25\degree>$ and $<12\cos337\degree,\ 12\sin337\degree>$ .

a)

$<4.37,\ 6.97>$

b)

$<20.11,\ -0.46>$

c)

$<20.11,\ 8.91>$

d)

$<7.52,\ -3.21>$

11.

Find the magnitude of the resultant of these two vectors: $\left(4i+3j\right)$ and $\left(2i-7j\right)$ .

a)

$2\sqrt{13}$

b)

$52$

c)

$10$

d)

$2\sqrt{10}$

12.

Which of these represents the vector with a magnitude of 6 and direction angle of 38^o?

a)

$4.73i+3.69j$

b)

$3.69i-4.73j$

c)

$-4.73i-3.69j$

d)

$-3.69i+4.73j$

13.

Which of the following is the component form of $\overrightarrow{AB}$ with initial point $A\left(-5,3\right)$ and terminal point $B\left(2,-1\right)$ .

a)

$<4,-1>$

b)

$<7,-4>$

c)

$<7,4>$

d)

$<-6,4>$

14.

Given $B=<7,-3>$ $U=<-3,3>$ $C=<0,-5>$ , solve:

___________- B = U.

a)

$<-10,6>$

b)

$<10,-6>$

c)

$<-4,0>$

d)

$<4,0>$

15.

Given $B=<7,-3>$ $U=<-3,3>$ $C=<0,-5>$ , find the direction angle of vector C.

a)

Undefined, does not exist.

b)

$90\degree$

c)

$180\degree$

d)

$270\degree$

16.

Graph $R=2B-C\$ using the vectors above.

a)

b)

c)

d)

17.

An airplane traveling directly northwest has airspeed of 450 kilometers per hour. The wind velocity is 40 kilometers per hour in the direction S 30^o W. Find the resulting speed of the plane.

a)

441.34 kph

b)

461.97 kph

c)

411.49 kph

d)

438.27 kph

18.

An airplane traveling directly northwest has airspeed of 450 kilometers per hour. The wind velocity is 40 kilometers per hour in the direction S 30^o W. What is the direction angle?

a)

$320.02\degree$

b)

$140.02\degree$

c)

$139.80\degree$

d)

$136.44\degree$

19.

If a plane is flying with a direction angle of 289.12^o, what is its bearing?

a)

S 19.12^o W

b)

N 160.88^o E

c)

E -70.84^o S

d)

S 19.12^o E

20.

Two ships leave port at 4 pm. One is heading at a bearing of N 38^o E and is traveling at 11.5 miles per hour. The other is traveling 13 miles per hour at a bearing of S 47^o E. How far apart are they when dinner is served at 6 pm?

a)

18.09 miles

b)

36.18 miles

c)

80.96 miles

d)

48.71 miles

Vectors Assessment

Total questions: 20

Worksheet time: 46mins

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