Vectors Questions and Answers

Glven Two Points Write the equation of the line with the two given points 5 1 3 and 3 5 6 1 4 and 6 1

Given the triangle below find tan 0 Enter the answer as a fraction Provide your answer below 3 4 5 0

4 Given Prove O 1 2 3 4 A B C m AOB m 1 m BOC m 1 OB bisects LAOC Statements 1 PROOF Reasons 1 Given 2 Substitution 3 Angles with equal measures are congruent 4 If a ray divides an angle into two congruent angle then the ray bisects the angle

If we write the following complex number in standard form then b Your answers here have to be simplified so that the 2 131 2 13i a bi

Suppose that AB AC AD AE and AF are coplanar F A B D E

Reduce the spanning set to a basis for R S 2 2 1 3 2 1 2 3 0 0 2 1

Suppose is the function defined by f x Ax where a The domain of fis R4 A 6 4 3 B 0 2 1 1 C 4 0 1 1 D 0 0 1 0 E 9 0 3 F 18 4 6 6 3 9 0 1 1 2 1 3 For instance enter R 5 for R5 b The codomain off is R3 For instance enter R 5 for Rs c Select all of the vectors that are in the kernel of f You should be able to justify your answers there may be more than one correct answer 3 A 0 A 4 0 1 1 B 0 2 1 1 C 0 0 1 0 D 9 0 3 E 184 63 d Select all of the vectors that are in the image of f You should be able to justify your answers there may be more than one correct answer

List the angles in order from least to greatest measure 9 E 10 11 X 9 cm D 15 cm 12 cm 3 0 m G 1 1m H 2 0 m 28 ft 19 ft 21 ft

6 CE 8 6 20 2 6 8 N Sequence 1 Figure 1 Is first reflected over the line y and then translated 8 units up and 2 units right to create figure 2 co Which two sequences of transformations could be used to prove figure 1 and figure 2 are congruent Sequence 3 Figure 1 is first reflected across the x axis X Sequence 2 Figure 1 is first translated down 10 units and then rotated 180 clockwise about the origin to create figure 2 Sequence 4 Figure 1 is first rotato 009

A 8 12 8 Determine the following cardinalities n A n C 19 n An C n AUB 21 n AUBUC n An BnC Help 7 7 Video B

Find a matrix P such that PTAP orthogonally diagonalizes A Verify that PTAP gives the proper diagonal form Enter each matrix in the form row 1 row 2 where each row is a comma separated list A P PT AP 0 10 10 10 5 0 10 0 5 2 1 1 1 3 2 2 1 0 0 0 0 15 0 0 0 15 X

A 1 2 3 4 6 12 B 2 4 6 8 10 12 C 1 3 5 7 9 11 U 1 2 3 4 5 6 7 8 9 10 11 12 What is An C A 1 3 B 2 4 6 8 10 12 C 1 2 3 4 5 6 7 9 11 12

Find the sum of each series 3 6 12 24 768 For the toolbar press ALT F10 PC or ALT FN F10 Mac

Find the scalar and vector projections of b onto a a 3 6 2 b 3 2 1 comp b proj b

Wire 1 41 34 ft 38 Wire 2 Based on the given information answer the questions below Round each answer to the nearest tenth Part A How tall is the pole Show your work Part B How far from the base of the pole does Wire 2 attach to the ground Show your work Part C How long is Wire 1 Show your work

If b 15 7 then 1 6 9 8 7 5 6 5 LG

Vectors can be Select one or more a scaled b subtracted c inverted Od squared

The poin L A m O A LU B C D E F B in the graph below represents 4 5 25 O E 3 N D

If A JHI AJLK then what does JH OZK OLK KJ

Match each statement with its symbolic notation G A q P B pq C pv q D p q E q p F p q G 4 Conjunction 5 Disjunction 6 Conditional 7 Inverse 8 Converse 9 Contrapositive 10 Riconditional n a

b B M D C a In the above diagram OA a and OB b C lies on 04 where OC the midpoint of AB BC and OD intersect at M i Express the following vectors in terms of a and b A AD B OM Hence evaluate BM MC OA D is 3 marks 3 marks 4 marks

3 For independent random creams produced in two different factories the amount of fat was measured and summary statistics are given below Assume that the fat content is normally distributed Factory Factory B n Y S 13 31 2 2 5 11 30 8 3 4 a It is suspected that the creams produced in factory A are higher than the fat content of creams produced in factory B a 0 05 Write Ho and Ha take the test and interpret 20 points b Calculate the significance level of the test 10 points

Solve for x Round to the nearest tenth when necessary 1 5 1 14 5

Let 2 X 1 3 1 Y 1 11 2 5 0 31 V 2 13 x 1 U 1 W 2 02 a 3 marks XYT T b 2 marks 2Y I3 c 4 marks tr W V 2 1 2 1 0 1 0 Evaluate each of the following if possible If it is not possible justify your answer Show all your work

Writing Linear and Exponential Equations An investment is initially worth 11 600 Write an equation representing the value of this investment V after t years in each of the following situations a The value decreases by 6 per year b The value decreases by 800 per year c The value increases by 633 per year d The value increases by 12 per year NY1 V V V V

Based on the information given can you determine that the quadrilateral must be a parallelogram Explain Given XN NZ and NY NW Y W X N 2 Yes opposite sides are congruent Yes two opposite sides are both parallel and congruent No you cannot determine that the quadrilateral is a parallelogram Yes diagonals of a parallelogram bisect each other

Joanna needs two spools of ribbon but there are 13 different choices In how many ways can she choose 2 different spools of ribbon

Find the angle between vectors 2 5 and 3 1 Select one a 130 2 b 49 8 OC Do not have enough information d 54 04

a and fb are orthogonal If a 4 5 and b x y then the ratio 0 is

If a 1 4 b 3 6 what is a b Choose the correct vector Select one a b O C 22 00 16 14 12 10

Because 3i 2j 2 5j and 27 5j 3i 2j i i we can conclude that vector addition is

Given the vector with magnitude 12 and directional angle 60 Write the vector in unit vector form JI 49 S

3 5 The vector above has a magnitude of 1 18 O

Given the vector 4 8 4 8 with a directional angle of

her the equation y 9 x is linear Find the

Consider the vectors in 3 space a b c such that 35 2b 4c 0 then it is necessarily true that O a a 0 b 3x b c c ax b d a b c 0 c 0

Siven polynomial is below f x x 4x 6x 36 a 2 is a zero List all the zeros of the function Enter your answers as a comma separated list X b Write the polynomial as the product of linear factors f x

Given the vector 6 12 6 12 with a directional angle of

Given the graph of two vectors choose the image which best represents the difference of u Hint Graph the vectors on graph paper then draw the resultant vector Select one a 4 4 4 k

Given a vector begins at 2 3 and ends at 2 then the components of the vector are 4

Next question You can retry this question below Points A and B are separated by a lake To find the distance between them a surveyor locates a point C on land such than ZCAB 44 3 Find the distance across the lake from A to B C Get a similar question 459 yd distance B 315 yd NOTE The triangle is NOT drawn to scale yd 1 44 3 Enter your answer as a number your answer should be accurate to 2 decimal places Question Help Worked Example 1 A

Find a constant h for which the vectors 3 and h are orthogonal 6 pts

Find the measure of ZPQR List in sequence with reasons the angles you had to find along the wa o determine the required angle M 50 N S 17 P 80 R O

3 Estimate a polynomial for the sine function using the points sin0 0 sin 1 2 1 and sin 0 Hint rewrite as points in x y form to look more like the last problem Use your result to estimate sin 7 3

The graph of a linear function f is shown a Identify the slope y intercept and x intercept b Write the equation that defines f The slope is Type an integer or a simplified fraction Ay 61 10 8 64 2 44 6 B E

For problems 8 10 solve the triangles Round to the nearest tenth 67 V 49 50ft

Match each symbol to the corresponding vocab words from set theory CCB a Intersection An B AUB AC b Union c Subset d Complement

Find the angle between the vectors u 6i 6j v i 3j 5k The angle between the vectors is 0 Round to the nearest hundredth as needed radian s

Sunflower oil is a cooking ingredient that can be used as a substitute for olive oil The density of sunflower oil is 0 925 grams per cubic centimeter A farmer would like to sell bottles of sunflower oil that contain 370 grams of oil What is the volume of the smallest container that holds 370 grams of oil O 0 0025 cubic centimeters O 27 75 cubic centimeters O342 25 cubic centimeters O 400 cubic centimeters

Enjoys playing video games Does not enjoy playing video Plays an organized sport 31 22 Does not play an organized sport 32 15 games One of these 100 students is selected at random to give more detailed answers to some follow up questions A What is the probability that the chosen student enjoys playing video games or plays an organized sport B What does P Enjoys playing video gamesldoes not play an organized sport represent for this survey C Calculate the value of P Enjoys playing video gamesldoes not play an organized sport