Results 1 to 2 of 2

Math Help - Vector problem

  1. #1
    Junior Member
    Joined
    Mar 2009
    Posts
    41

    Vector problem

    Three vectors , , and each have a magnitude of 47 m and lie in an xy plane. Their directions relative to the positive direction of the x axis are 34, 191, and 313, respectively. What are (a) the magnitude and (b) the angle of the vector + + , and (c) the magnitude and (d) the angle of - + ? What are (e) the magnitude and (f) the angle of a fourth vector such that ( + ) - ( + ) = 0?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,397
    Thanks
    1327
    Quote Originally Posted by BiGpO6790 View Post
    Three vectors , , and each have a magnitude of 47 m and lie in an xy plane. Their directions relative to the positive direction of the x axis are 34, 191, and 313, respectively. What are (a) the magnitude and (b) the angle of the vector + + , and (c) the magnitude and (d) the angle of - + ? What are (e) the magnitude and (f) the angle of a fourth vector such that ( + ) - ( + ) = 0?
    The simplest way to do this is to calculate the x and y components of each vector and add "component-wise".
    Since \vec{a} has magnitude 47 and makes an angle of 34 with the x-axis, you can think of this as a right triangle with hypotenuse 47 and angle 34. The x-component is the "near side" and so is 47 cos(34). The y- component is the "opposite side" and so is 47 sin(34).

    Similarly, \vec{b} has x-component 47cos(191) and y-component 47sin(191) (both are negative) and \vec{c} has x-component 47cos(313) and y-component 47sin(313).

    Now you know that \vec{a}+ \vec{b}+ \vec{c} has x-component 47(cos(34)+ cos(191)+ cos(313)) and y-component 47(sin(34)+ sin(191)+ sin(313)). Knowing the x and y components, the magnitude is the square root of the sum of the squares of the components and the angle it makes with the x-axis is arccos(x-component/magnitude)= arcsin(y-component/magnitude). Be careful of the signs- your calculator will only give the principle arcsine and arccosine.

    Similarly, \vec{a}- \vec{b}-\vec{c} has x-component 47(cos(34)- cos(191)- cos(313)) and y- component 47(sin(34)- cos(191)- cos(313)).

    Finally, \vec{d} such that (\vec{a}+ \vec{b})- (\vec{c}+ \vec{d})= 0 is given by \vec{d}= \vec{a}+ \vec{b}- \vec{c} and has x-component 47(cos(34)+ cos(191)- cos(313)) and y-component 47(sin(34)+ sin(191)- sin(313)).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. vector problem
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 10th 2011, 10:17 AM
  2. 3D vector problem
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: May 6th 2011, 08:59 AM
  3. Vector problem
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 3rd 2011, 03:39 PM
  4. vector problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: March 9th 2010, 08:34 AM
  5. vector problem sum
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 9th 2009, 08:42 AM

Search Tags


/mathhelpforum @mathhelpforum