SOLUTION: Let u=−3i+j+k and v=mj+nk, where m, n∈ . Given that v is a unit vector perpendicular to u, find the possible values of m and of n.

Algebra ->  Functions -> SOLUTION: Let u=−3i+j+k and v=mj+nk, where m, n∈ . Given that v is a unit vector perpendicular to u, find the possible values of m and of n.      Log On


   

Question 1193904: Let u=−3i+j+k and v=mj+nk, where m, n∈ . Given that v is a unit vector perpendicular to u, find the possible values of m and of n.
Answer by ikleyn(52787) About Me  (Show Source):
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Let u=−3i+j+k and v=mj+nk, where m, n∈ .
Given that v is a unit vector perpendicular to u, find the possible values of m and of n.
~~~~~~~~~~~~~~~ 

Since vectors u and v are perpendicular, their scalar product is zero.

It gives first equation

    m + n = 0.         (1)


Since vector v has the length of 1, it gives you second equation

    m^2 + n^2 = 1.     (2)


From (1), express  m = -n and substitute into (2). You will get

    (-n)^2 + n^2 = 1

          2n^2   = 1

           n = +/- sqrt%282%29%2F2.


ANSWER.   There are two possibilities:

          (a)  m = sqrt%282%29%2F2%29,  n = -sqrt%282%29%2F2%29,

    and/or

          (b)  m = -sqrt%282%29%2F2%29,  n = sqrt%282%29%2F2%29.

Solved.