Questions on Algebra: Introduction to vectors, addition and scaling answered by real tutors!

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Question 1028187: 1) If p=2i-3j, q=3i+5j and r=i+j find 2p+q-3r.
2) The position vectors of the points P,Q,R and S relative to the origin O are: P=Si-6j, Q=4i+4j, R=8i-9j, S=10i-25j respectively,
I) 5p-3q+4r
Thank you :)

Click here to see answer by Edwin McCravy(20055)

Question 1028572: Find the sequence of transformations which takes the graph
y=1/x^2 to y=2/(4x+3)^2 -1

Click here to see answer by Edwin McCravy(20055)

Question 1028572: Find the sequence of transformations which takes the graph
y=1/x^2 to y=2/(4x+3)^2 -1

Click here to see answer by AnlytcPhil(1806)

Question 1028867: Find the inverse function of f:[3,∞) -> R, f(x) = (x-4)^2 +1
Why does the domain of f need to be restricted to [4,∞) in this question?
Click here to see answer by jim_thompson5910(35256)

Question 1028926: The position vectors of the points p,q,r and s relative to the origin O are: p=si-6j, q=4i+4j, r=8i-9j, s=10i-25j respectively.
Solve:
I) 5p-3q+4r

Click here to see answer by Alan3354(69443)

Question 1029317: Write the vector as a linear combination of the standard unit vectors i and j.
Initial Point is (-1,2) and Terminal Point is (6, -5).

My answer is 7i - 7j but it says I got it wrong, what is this?
I did the work (6-(-1)) + (5-(-1), so this becomes 7i + (-7j) = 7i - 7j..
Click here to see answer by ikleyn(52781)

Question 1031404: Find the rule of the cubic function that passes through the points (-5,0), (2,0), (3,0) and (0,20). Give your final answer in the form y=ax^3+bx^2+cx+d.
Click here to see answer by Fombitz(32388)

Question 1033676: Statement: Find the unit vector having the same direction as v (the v is a vector for it is bolded in the textbook)
Problem: v = 5i (i is a vector)

Click here to see answer by stanbon(75887)

Question 1036725: Please help me solve this vectorial problem :
U= 2i+aj
V= 3i+(a-2)j
Find a=?
Click here to see answer by Fombitz(32388)

Question 1037930: A boat travels 19 nautical miles in a direction N 30 E and then travels 25 nautical miles south-east. Express each of these displacements in component form (East and North) and hence find the displacement for the whole journey in polar form.
Click here to see answer by Alan3354(69443)

Question 1039894: Jessica stretches her arms out 0.6 m from the center of her body while holding a 2 kg mass in each hand. She then spins around on an ice rink at 1.1 m/s.
a.What is the combined angular momentum of the masses?

Click here to see answer by KMST(5328)

Question 1039895: Jessica stretches her arms out 0.6 m from the center of her body while holding a 2 kg mass in each hand. She then spins around on an ice rink at 1.1 m/s.
If she pulls her arms in to 0.15 m, what is her linear speed if the angular momentum remains constant?
Click here to see answer by KMST(5328)

Question 1039893: Each year at a college, there is a tradition of having a hoop rolling competition. Alex rolls his 0.25 kg hoop down the course. If the hoop has a radius of 0.5 m, what is the moment of inertia of Alex�s rolling hoop?
Click here to see answer by macston(5194)

Question 1040014: 1. A 25 N object requires a 5.0 N to start moving over a horizontal surface. What is the coefficient of static friction?

2.A 12 N cart is moving on a horizontal surface with a coefficient of kinetic friction of 0.20. What force of friction must be overcome to keep the object moving at a constant velocity?

Click here to see answer by solver91311(24713)

Question 1040630: U=(9,2) v=(-5,-2) 2u-3v=?
Click here to see answer by jim_thompson5910(35256)

Question 1041269: Let CC and DD be points with position vectors c and d respectively. If |c|=5, |d|=7 and c⋅d=4, find vector|CD|
How can i handle this problem?
Thank you so much
Click here to see answer by robertb(5830)

Question 1043003: Find a unit vectornormal to the surmal x cube+ycube+3xyz at thepoint( 1,-2,1)

Click here to see answer by ikleyn(52781)

Question 1043127: Transform the vector shown so that it's half the length. What is the x-value of the terminal point of the resulting vector?
Graph:
a line to (8,7) from 0
Click here to see answer by ikleyn(52781)

Question 1043241: The position vector of OP, OQ and OR is <0,0,0>, <1,2,3> and <2,1,-1> respectively. Find
i) the area of the triangle PQR
ii) the projection of QR and OR
iii) the direction angles of vector QR
Click here to see answer by Edwin McCravy(20055)

Question 1043484: Find all values of k such that the triangle in R3 with vertices
A = (1, 3, 1), B = (0, 5, 2), C = (k, 3, 1)
is a right angled triangle.
Click here to see answer by robertb(5830)

Question 1043770: Find all values of k such that the triangle in R3 with vertices
A(1,3,-1), B (0,5,-2), C(k,3,1) is a right angle triangle
Click here to see answer by josgarithmetic(39617)

Question 1045096: what is a group? And construct three example of groups.
Click here to see answer by ikleyn(52781)

Question 1045099: Is a set a group, if and only if it is a ring? Give an example in each case.
Click here to see answer by ikleyn(52781)

Question 1045479: Determine the equation of the tangent plane to the sphere x^2 + y^2 + z^2 = 1 at the point (1/2, 1/2,).
Click here to see answer by Edwin McCravy(20055)

Question 1046967: A gnat takes off from one end of a pencil and flies around erratically for 30.1 seconds before landing on the other end of the same pencil. If the gnat flew a total distance of 1.65 meters, and the pencil is 0.0563 m long, find the gnat\'s average speed, as well as the magnitude of the gnat\'s average velocity vector.
Click here to see answer by Edwin McCravy(20055)

Question 1047194: Can anyone help me with this math problem?�Provide�an�example�of�a�subset�of�R2�that�is�a�nontrivial�subspace�of�R2.
Click here to see answer by ikleyn(52781)

Question 1048504: Please solve the equation sin*(2*x+(pi/3)) = 1/2 for x is [0,pi] Show working
Click here to see answer by josmiceli(19441)

Question 1048622: I need to show�an�example�of�a�subset�of�R2�that�is�a�nontrivial�subspace�of�R2. Then I need to prove that it is nontrivial. Can someone please help me.
Thanks.
Click here to see answer by ikleyn(52781)

Question 1049494: u=3i+2j-k, v=i-3j+2k, find the unit vector in the direction of u-2v.
Click here to see answer by Edwin McCravy(20055)

Question 1050772: How do I show proof for this problem?
If u∈V, then 1u=u
I have the following:
Let u= (a1, a2) where a1 and a2 are real numbers.
1(X)= [a1, a2] by substituting the coordinates in vector form.
1[a1,a2] = [1a1,1a2] by definition of scalar multiplication'
[1a1, 1a2] = [a1, a2] by definition of multiplicative identity of real numbers.
[a1, a2] = X by substitution.
Can anyone tell me if I did this correctly or if not please help me out.

Click here to see answer by rothauserc(4718)

Question 1057010: Show that the points A(1,0,2), B(3,-1,3), C(4,2,1) and D(2,3,0) are the vertices of a parallelogram.
Click here to see answer by Alan3354(69443)

Question 1058404: If A and B are 3�6 matrices, and CC is a 9�3 matrix, which of the following are defined?
A. A+C
B. CA
C. BC
D. B-A
E. CB-A
Click here to see answer by jim_thompson5910(35256)

Question 1058402: Hey Guys I'm currently stuck with this problem. I was able to solve (a) already but (b) is giving me a hard time.
A man wishes to row the shortest possible distance from north to south across a river which is flowing at 3 km/hr from the east. He can row at 4 km/hr.
(a) In which direction should he steer?
At an angle (in degrees) of 48.59025877 east of south.
(b) Suppose that when the man is in the middle of the river, a wind of 5 km/hr from the southwest starts.
In which direction should he steer to move straight across the river?
At an angle (in degrees) of XXXX west or east of south.
Which bank of the river will the rower reach first?
The south bank, the north bank or neither.
Click here to see answer by Alan3354(69443)

Question 1060048: For the Initial point of (1,11) and the Terminal point of (9,3), how would you find the component and magnitude?
Click here to see answer by jim_thompson5910(35256)

Question 1061324: Find the work done by a force of 8 pounds acting in the direction of 44� to the horizontal in moving an object 7 feet from (0, 0) to (7, 0). Round answer to the nearest tenth of a foot-pound.
Click here to see answer by ikleyn(52781)

Question 1062030: Let P be a projection, so . If , compute .
Click here to see answer by ikleyn(52781)

Question 1062725: What is the direction and magnitude of v = < -3.5, -12>
Click here to see answer by math_helper(2461)

Question 1062807: Find the components of vector w, with ||w|| = 8 and θ = -150o.
Click here to see answer by ikleyn(52781)

Question 1062807: Find the components of vector w, with ||w|| = 8 and θ = -150o.
Click here to see answer by Edwin McCravy(20055)

Question 1062806: What is the direction and magnitude of a = 6i + 8j?
Click here to see answer by ikleyn(52781)

Question 1066603: Find the specified vector or scalar.
u = -4i + 1j and v = 4i + 1j; Find .u+v
A. sqrt34

B. 8
C. 5
D. 2
Click here to see answer by Fombitz(32388)

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