calculus

posted by .

Find two unit vectors that make an angle of 60° with v = ‹3, 4›. Give your answers correct to three decimal places.

I'm not sure what to do here; I believe that I use to definition of a dot product (or maybe cross product) with relation to the trig function (cos for dot, sin for cross) but for whatever reason I can't get my answer to come out.

  • calculus -

    let such a vector be (a,b)
    then (a,b)⋅(3,4) = |(a,b)||(3,4)|cos60°
    3a + 4b = 5√(a^2 + b^2)(1/2)
    6a+8b = 5√(a^2+b^2)
    let a= 1 , any non-zero number will do
    6+8b = 5√(1+b^2)
    square both sides
    36+96b +64 b^2 = 25 + 25b^2
    39b^2 + 96b + 11 = 0
    b = (-96 ± √7500)/48
    = appr. -2.341 or -0.1205

    so two vectors could be (1, -2.341) or (1, -.1205)
    but you want a unit vector, so using the second point,
    |(1,-.1205)| = 1.00723

    giving us a unit vector of (1/1.00723 , -.1205/1.00723)
    or appr. (.9928 , -.1196)

    check:
    (3,4).(.9928,-.1196) = 2.5
    |(3,4)||(.9928,-.1196)cos60 = 2.5

    reverse the direction of the above vector to get
    (-.9928, .1196) for a second vector, or
    let a = some other value and repeat the above steps

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    Find two unit vectors that make an angle of 60° with v = 3, 4 (Enter your answer as a comma-separated list of vectors. Round your answers to four decimal places.)
  2. math

    Three hundred twelve viewers were asked if they were satisfied with TV coverage of a recent disaster. Gender Female Male Satisfied 90 53 Not Satisfied 124 45 (a) Find P(satisfied). (Give your answer correct to two decimal places.) …
  3. Math/Statistics

    Three hundred twelve viewers were asked if they were satisfied with TV coverage of a recent disaster. Gender Female Male Satisfied 90 53 Not Satisfied 124 45 (a) Find P(satisfied). (Give your answer correct to two decimal places.) …
  4. math

    Consider the following bivariate data. Point A B C D E F G H I J x 3 4 2 1 7 2 1 0 4 2 y 1 7 3 3 6 6 5 0 6 2 (a) Construct a scatter diagram of the given bivariate data. (Do this on paper. Your instructor may ask you to turn in this …
  5. math help

    Can some one help me with this one??? Consider the following bivariate data. Point A B C D E F G H I J x 3 4 2 1 7 2 1 0 4 2 y 1 7 3 3 6 6 5 0 6 2 (a) Construct a scatter diagram of the given bivariate data. (Do this on paper. Your
  6. math check

    A machine produces parts with lengths that are normally distributed with ó = 0.52. A sample of 16 parts has a mean length of 75.07. (a) Give a point estimate for ì. (Give your answer correct to two decimal places.) 75.07. (b) Find …
  7. statistics

    Consider the following bivariate data. Point A B C D E F G H I J x 3 4 2 1 7 2 1 0 4 2 y 1 7 3 3 6 6 5 0 6 2 (b) Calculate the covariance. (Give your answer correct to two decimal places.) (c) Calculate sx and sy. (Give your answers …
  8. statistics check

    Consider the following bivariate data. Point A B C D E F G H I J x 3 4 2 1 7 2 1 0 4 2 y 1 7 3 3 6 6 5 0 6 2 (b) Calculate the covariance. (Give your answer correct to two decimal places.) 5.35 was my answer . (c) Calculate sx and …
  9. statistics help

    Complete the hypothesis test with alternative hypothesis ƒÊd ‚ 0 based on the paired data that follows and d = O - Y. Use ƒ¿ = 0.01. Assume normality. Oldest 188 174 192 196 65 Youngest 186 168 199 199 69 (a) Find t. (Give …
  10. math

    Consider the following bivariate data. Point A B C D E F G H I J x 3 4 2 1 7 2 1 0 4 2 y 1 7 3 3 6 6 5 0 6 2 (a) Construct a scatter diagram of the given bivariate data. (Do this on paper. Your instructor may ask you to turn in this …

More Similar Questions