science (physics) Need to solve this today please

(a) Express the vectors A, B, and C in the figure below in terms of unit vectors.

(b) Use unit vector notation to find the vectors R = A + B + C and S = C – A – B.

(c) What are the magnitude and directions of vectors R and S?

Well the picture goes and has a vector
A pointing in the 1st quadrant of the graph and between the y axis it has a angle of 37 deg
and a magnitude of 12m

vector B is in the 4th quadrant and the angle from the x axis to the vector is 40 deg
and a magnitude of 15m

vector C is in the 3rd quadrant and measured from the x axis it's angle is 60 deg
and a magnitude of 6.0m

~What are unit vectors? Would that just refer to the m? And does that include the i, j, and k hat? (i [^ on top of i])

How would I find these? like for C it has the angle of 60 deg from the x axis in the 3rd quadrant but if I was finding the x component of C I wouldn't use 60 right for the angle but rather 180+60 = 240 deg.
I'm not sure if that's correct but that has gotten me confused with unit vector.

And for the B vector in the 4th quadrant wouldn't I find the x and y component using not 40 deg but rather -40 deg?

I really need to solve this by today...

  1. 👍
  2. 👎
  3. 👁
  1. From your description, and lettng i and j be unit vectors along the +x and +y axes,
    A = 12.00 (sin 37 i + cos 37 j)
    = 6.00 i + 9.58 j
    B = 15.00 (cos 40 i - sin 40 j)
    = 11.49 i - 9.64 j
    C = 5.00 (-cos 60 i -sin 60 j)
    = -2.50 i - 4.33 j
    The changes of sign here and there, and the switch from sin to cos for i, are due to your changing definition of the quadrant the vector is in and the changing reference axis (y for A, +x for B and -x for C).

    Now that you have defined A, B, and C with unit vectors, the calculation of R = A+B+C and S = C-A-B is easy. Once you have R & S in unit vector notation, switch back to magnitude/angle notation

    1. 👍
    2. 👎
  2. Why is
    A = 12.00 (sin 37 i + cos 37 j)
    = 6.00 i + 9.58 j ??

    I got when I plugged it into my calculator in degrees mode
    7.22 i + 9.58 j

    Well for
    R= A+ B + C

    R= (7.22i + 9.58j) + (11.49i- 9.64j) + (-2.50i - 4.33j) = (16.21i - 4.39j)m

    S= C-A-B

    S= (-2.50i - 4.33j)- (7.22i + 9.58j) - (11.49i - 9.64j)=
    -2.50i - 4.33j- 7.22i - 9.58j -11.49i + 9.64j= (-21.21i- 4.27j)m

    For step
    c.) I don't know how to switch back to magnitude/ angle notation...does that include using tan ?

    1. 👍
    2. 👎
  3. Um PLEASE help me out on this part c..seriously ...I did show what I did for a and b and I just need to know how c would work...

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics

    Three vectors are shown in the figure. Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. Give the resultant in terms of (a) magnitude and (b) the angle within the positive x axis.

  2. Calculus and Vectors


  3. Math

    if vectors a+2b and 5a-4b are perpendicular to each other and a and b are unit vectors. Find the angle between a and b.

  4. vectors

    Express the unit vectors iˆ, jˆ, and kˆ as ordered triples and show that: a) iˆ x jˆ = kˆ b) kˆ x jˆ = -iˆ To begin, I subbed in iˆ= (1,0,0) jˆ= (0,1,0) kˆ = (0,0,1) for a) I got (0,-1,1) = (0,0,1) after crossing

  1. physics

    Two workhorses tow a barge along a straight canal. Each horse exerts a constant force of magnitude F, and the tow ropes make an angle θ with the direction of motion of the horses and the barge. (Figure 1) Each horse is traveling

  2. Calculus

    Given vectors u= (1,-1,3) and v= (-4,5,3) find an ordered triple that represents vectors 3u-2v. a.(16,1,-7) b.(11,-13,3) c.(10,-12,1) d.(7,-7,16) I don't want you to straight up give me the answer. I need someone to teach me how

  3. PreCalculus

    Given vectors u=7i + 3j and v = -4i + 3j, find 5u-4v in terms of unit vectors. I am just beginning the study of vectors and have this problem. Could someone help? Thanks.

  4. Physics

    The position of a particular particle as a function of time is given by r = ( 9.60ti + 8.85j - 1.00t^2 k)m, where t is in seconds. a) Determine the particle's velocity as a function of time. b) Determine the particle's

  1. Grade 12 Math

    if a and b are unit vectors, and magnitude of vectors a +b = sq. root of 3, determine (2a-5b) dot (b+3a).

  2. Physics

    A certain coaxial cable consists of a copper wire, radius a , surrounded by a concentric copper tube of inner radius c . The space between is partially filled (from b out to c ) with material of dielectric constant K. The goal of

  3. mathematics

    given vectors u=-9i+8j and v=7i+5j find 2u-6v in terms of unit vectors i and j

  4. Digital art

    Lesson 1: Final Exam 0103000 M/J Digital Art and Design 1- T2 Unit 5: Final Exam. I have been stuck on this 50 question test for a while now im willing to give away a gift card if someone helps me and puts in the answers by typing

You can view more similar questions or ask a new question.