Free Printable UNIT VECTORS

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UNIT VECTORS

Total questions: 24

Worksheet time: 35mins

Name

Class

Date

A unit vector is a vector that is parallel to the given vector and has _____________.

magnitude of 1

the same direction

the same size

Step 3: Find the unit vector for < 4,5 > .

You will find 2 answers, 1 decimal one in standard form.

< 4 / √41 , 5 / √41 >

< .62, .78>

< .10, .12 >

Find the unit vector in the direction of <4, -3>

< ⅘, -⅗ >

<0.57, -0.43>

<1, -1>

-¾

A unit vector is a vector that is _____________the given vector and has _____________.

parallel to, magnitude of 1

equal to, the same direction

opposite, the same size

smaller than, the same direction

Find the unit vector in the direction of <-7, 0>

-7

-1

<-1, 0>

<1, 0>

Find the component form of a vector whose initial point is (5, 7) and terminal point is (1, 10)

<-4,3>

<4,-3>

<6,17>

Determine the direction of the vector <-1, 3>

161 degrees

-72 degrees

288 degrees

108 degrees

Using degrees only, what is the direction of the vector?

220^o

230^o

310^o

320^o

the direction (θ) for vector v. Round to three decimals.

-74.054^o

105.945^o

-15.945^o

164.055^o

10.

The dot product $\left(1,\ -2,\ 2\right)\cdot\left(-1,\ 1,\ 3\right)$ is equal to

None of the above

11.

A $\cdot$ B = 0 means that

A and B are colinear

A and B are parallel

A and B are perpendicular

None of the above

12.

The cross product of two vectors A and B is another vector

True

False

13.

Select all that apply for the cross product:

It is commutative, i.e.,

A $\times$ B = BA

The distributive law is valid, i.e.,
Aundefined(B + C) = AundefinedB + AundefinedC

C = AundefinedB is perpendicular to both A and B

It may be multiplied by a scalar $m$ without changing its direction

14.

Which symbol is used to show vector quantities?

Triangle

Line

Arrow

15.

What is magnitude?

The direction that describes a quantity.

A numerical value

A unit of force

16.

Which of the following is an example of scalar magnitude?

velocity

mass

acceleration

force

17.

The _______ of two or more vectors is the sum of the vectors.

components

scalar

resultant

magnitude

18.

Vector a = 2i + 3j - 5k. What is the value of 3a?

3i + 3j - 3k

5i + 6j - 8k

6i + 9j -15k

6i + 6j - 15k

19.

Given points A(3, 2, -4) and B(2, 1, -1), so the vector AB is

i + 3j -5k

-i -3j +3k

i -j -5k

-i -j +3k

20.

Find the angle between vectors <1,3> and <2,-5>.

40.24°

49.76°

139.76°

92.57°

21.

Find the dot product of <1, -2> and <3, 2>.

<3, -4>

<4, 0>

-1

22.

What is the angle between two orthogonal vectors?

180 degree

90 degree

60 degree

45 degree

23.

If ||v||= 8, ||w||=6 and the angle between them is θ = 240˚ $Find\ \overrightarrow{\ \ v}.\overrightarrow{\ \ w}$

-24

-48

24.

What vector gives the sum of these two vectors?

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UNIT VECTORS

Total questions: 24

Worksheet time: 35mins

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