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

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 Algebra: Introduction to vectors, addition and scaling Solvers Lessons Answers archive Quiz In Depth

 Question 2451: I need to prove that the vectors u,v and w are in the span(u,v,w). I don't really know where to start. Any help would be appreciated. Thanks! Click here to see answer by khwang(438)

 Question 21755: Three forces, each of which is perpendicular to the other two, act on an object. If the magnitude of these forces are 6N, 10N, and 15N respectively, find the magnitude and direction of the resultant, and thier angles. Click here to see answer by Paul(988)

 Question 27347: Hi Triangle ABC has a right angle at A where AB= [-3] [ 3] [-2] and where CA= [-1] [ 3] [ 6] {the above vectors should each be in a long square bracket} a) Calculate the acute angle at B b) Find the length at AB I have a total blank on this question. I think the acute angle at B is 45 degrees,as it's a right angle triangle, but I don't know how to prove it using the vector information given. I think i have to find BC but I am stumped on how to do that, let alone find the length of AB. Please can you help? Thank you Click here to see answer by venugopalramana(3286)

 Question 30815: Given: The point A(x0, y0, z0) lies outside a plane Q with equation ax+by+cz+d=0. The point P(x, y, z) lies on the plane Q. AB is the distance between the point A and the plane Q (B is a point ON plane Q). Derive the equation: (AB)= | ax0+by0+cz0+d | / sq.root of (a^2+b^2+c^2). Basically, this question is asking you to derive the generality of finding the distance from a point to a plane. Any help is GREATLY appreciated, I would like it by tomorrow if possible!! Thanks, -Stephanie Click here to see answer by venugopalramana(3286)

 Question 31495: If vector x is denoted by V(x), If v(d)=p(V(a)XV(b))+q(V(b)XV(c))+r(V(c)XV(a)) and [V(a),V(b),V(c)]=1/8 then p+q+r is equal to A.8V(d)(V(a)+V(b)+V(c)) B.4V(d)(V(a)+V(b)+V(c)) C.8V(d) D.(V(a)+V(b)+V(c))V(d) Click here to see answer by venugopalramana(3286)

 Question 31721: Ok i'm not so worried about the sketches I just want confirmation about mainly part c and d. thank you.(~denotes an arrow) Adjacent sides of a triangle in R3 are formed by the vectors ~u = 3~i −2~j+~k and ~v = −~j+3~k. (a) With the aid of a rough sketch (not to scale and without axes) show clearly why the (scalar) component of ~u in the direction of ~v is given by ~u•~v/||~v||, and find this component. (b) Find a unit vector in the direction of ~v. (c) Find ~ p1, the vector projection of ~u on ~v. (d) Find vector ~ p2 orthogonal to ~v so that ~u decomposes into the sum ~ p1 + ~ p2. (e) Show and label ~ p1 and ~ p2 clearly on your rough sketch. Click here to see answer by venugopalramana(3286)

 Question 32098: Hi, 1) What rule do I use to find points on a plane when starting with an equation R3? Say 3x-3y+z=3 or any other equation for that mater. 2) How do I find the equation of a particular line in R3 in the form r = a + td. With a direction vector, and the coordinates of a point on a line. Click here to see answer by venugopalramana(3286)

 Question 33284: Let u={(x1,x2,x3)in R3|x1+x2+x3=a} for a in R3 fixed. Show the u is a vector subspace if and only if a=0. This abstract and I'm struggling on the abstract ideas in linear algebra. Thank you for any help you can give me!!! Click here to see answer by venugopalramana(3286)

 Question 33286: Suppose S,T are subspaces of V and s intersect T=0. Show that every vector in S + T can be written uniquely in the form A + B, with A in S, and B in T. Construct an example to show that this is false if S intersect T does not equal 0. Help, please!!! Thanks Click here to see answer by venugopalramana(3286)

 Question 34516: A straight line L and a plane P in R3 are defined by the equations 2x − 3y + z = 1 and (x, y, z) = (1,−1, 2) + t (1, 2, 3), t any real number. (a) Say briefly but clearly how you know the line L does not pass through the point (−1,−5,−3). (b) Say briefly but clearly how you know that the plane P does not pass through the origin. (c) Write the equation for the line perpendicular to the plane P and passing through the origin. (d) Write the equation for the plane perpendicular to L and passing through the point (0, 1, 3). (e) Write the equation for the xz-plane. Click here to see answer by venugopalramana(3286)

 Question 35432: A box contains some apples. Andree takes 1/2 of them along with one extra apple. Beatrice takes 1/3 of the remaining apples along but put 2 apples back in thebox & finally, corrine takes 5/6 of the remaining apples along with one more apple. There are now 7 apples left in the box. How many apples were in the box before Andree took her share? Click here to see answer by AnlytcPhil(1277)

 Question 35500: the vector u has magnitude 10 and bearing 200 degrees. vector v has magnitude 8 and bearing 35 degrees. choose the correct magnitude of u-v and its bearings. Click here to see answer by narayaba(40)
 Question 35500: the vector u has magnitude 10 and bearing 200 degrees. vector v has magnitude 8 and bearing 35 degrees. choose the correct magnitude of u-v and its bearings. Click here to see answer by venugopalramana(3286)

 Question 43415: write in polar form: negative sqroot of 5+i Click here to see answer by fractalier(2101)
 Question 43415: write in polar form: negative sqroot of 5+i Click here to see answer by venugopalramana(3286)

 Question 43408: what is the magnitude U: magnitude 1,850, bearing 125 degrees V: magnitude 2,960, bearing 25 degrees W: U+V Click here to see answer by fractalier(2101)

 Question 43411: what is the magnitude U: magnitude 23, bearing 215 degrees V: magnitude 14.5, bearing 105 degrees W: U+V Click here to see answer by venugopalramana(3286)

 Question 43406: find the magnitude U: magnitude 218, bearing 22degrees V: magnitude 170, bearing 112degrees W: U-V Click here to see answer by venugopalramana(3286)

 Question 43423: a plane flies 285 km due west and then 320 km due north. What are its distance and bearing from the starting point Click here to see answer by psbhowmick(529)

 Question 48321: Good evening, please could you help me in this physic euqation problem. I hop from you>>>> Find... Equation for electric potential that is the electrical equivalent at the gravitation potential equation.( "F"gravitational = gh ) Please. we need to find the equivalent equation> Poor student Modi Click here to see answer by longjonsilver(2297)

 Question 49846: a factor is to built on a lot measuring 180 ft by 240 ft. Building code specifies that a lawn of uniform width and equal in area to the factory must surround the factory. What must the width of this lawn be and what are the dimensions of the factory? Click here to see answer by venugopalramana(3286)

 Question 50437: Find a vector normal to the surface z + 2xy = x^2 + y^2 at the point (1,1,0). Normally I would use gradient g(x,y,z)=0 or f(x,y)= x^2 -2xy + y^2 -z but I can't make it work??? Click here to see answer by venugopalramana(3286)

 Question 54740: w = EI the problem wants a solution for I, and W is wattage, however, it does not state if it is 110 watt or 220 watt, E is for voltaqge and I is for resistance. My question is how do I know what the the resistance is if I don't know what the voltage is, (110/220W)? Can u help? Click here to see answer by ankor@dixie-net.com(15656)

 Question 67551: if i have 1200 feet of fencing what is the largest rectangular area i could have if i wanted to fence my backyard using the side of my house as a side? Click here to see answer by venugopalramana(3286)

 Question 69063: I have 61 horizontal lines; call them 1 through 61. Line 1 and line 61 are 375mm apart. I need to find the formula so that the distance between the lines increases by an exponential amount over the 375mm, the result being that the distance between 1 and 61 comes out at 375. That is the distances between lines increases, but by the same factor, until 61 is at 375mm. I hope I have explained this clearly. Thank you very much. Click here to see answer by stanbon(57361)

 Question 73597: I'm not sure if this is a vector problem or not, but this seemed like the closest in subject to the question to which I'm referring. Here's the question: My accurate watch has only one hand, an hour hand. At the precise moment that this hand points directly to the 22-minute mark, what is the exact time? (Disregard A.M. or P.M.) Click here to see answer by ankor@dixie-net.com(15656)

 Question 77893: I hope this is the correct category for this question. The chapter heading is Polar Coordinates:vectors. Convert to the appropriate equation. Given: Polar Coord. Form: r = 2 Cos [Theta] Find the Rectangular Coord. Form of this equation Help me please! Click here to see answer by scott8148(6628)

 Question 80905: From a cliff 385 ft above the sea a coastguard officer observed a sinking boat at an angle of depression of 21.o degrees. Closer to shore she saw a coastguard cutter at an angle of depression of 38.0 degrees. Find the distance between the coastguard cutter and the sinking ship. Click here to see answer by ankor@dixie-net.com(15656)

 Question 81010: Find the resultant using the component method for the given vectors A = 32degrees 3200lbs B = 36degrees 1300lbs C = 35degrees 2100lbs I added the 3 vectors using the head to tail method but not sure how to add three vectors, this is what I did: Ax =3200lb(cos32 degrees) =Ax = 2560 Ay = 3200(sin 32 degrees) =Ay = 1600 Bx = 1300lb (cos 36 degrees) = Bx = 1051.7 By - 1300 (sin 36 degrees) Its not finished but is that the way to do it? Click here to see answer by scott8148(6628)

 Question 81011: Two cables hold a 975 lb crate. The tension T1 and T2 equals 575lbs. Find ang le theta. I don't know if you can do this problelm without a picture. The picture is a thin long rectangular shape with T1 and T2 forming a triangle from this rectangle (the sides) and the crate (975lbs) is at the tip of the triangle. The angle theta is under the rectangular shape being the left and right angles of the triangle, if that makes sense? Click here to see answer by scott8148(6628)

 Question 83099: A helicopter is taking off vertically when a crate slips out of the cargo door. At that instant, the helicopter is moving upward at 15 m/s and is 50 m above the ground. What is the maximum height the crate will reach above the ground? After falling from the helicopter, how long will the crate be in the air? Please show work. Click here to see answer by ankor@dixie-net.com(15656)

 Question 83318: Question – 5: Consider the vectors,a=12i + 2j, b= -2i + 3j, and c = a-b (a) Find the magnitude, and the direction of the vectors a,b and c. (b) Find the value of the angle between a and b . (c) Find the area of the triangle whose vertices are the end points of the vectors, a , b , and c . Click here to see answer by stanbon(57361)