linear algebra

posted by .

Solve for x if the vectors (2, x, 7-x) and (x, 3, -2) are orthogonal

  • linear algebra -

    if orthogonal, then their dot product is zero

    (2,x,7-x) . (x , 3, -2) = 0
    2x + 3x - 14 + 2x = 0
    7x = 14
    x = 2

    (2,2,5).(2,3,-2) = 4 + 6 - 10 = 0

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    Find an orthonormal basis for the subspace of R^3 consisting of all vectors(a, b, c) such that a+b+c = 0. The subspace is two-dimensional, so you can solve the problem by finding one vector that satisfies the equation and then by constructing …
  2. Linear Algebra

    Hello ! i try to solve Linear algebra 2 questions(but need them be written properly as mathmatical proofs) Having A matrice nXn: 1)proove that if A^2=0 the columns of matrice A are vectors in solution space of the system Ax=0 (x and …
  3. Math - Vectors

    Prove that vector i,j and k are mutually orthogonal using the dot product. What is actually meant by mutually orthogonal?
  4. Linear Algebra, orthogonal

    The vector v lies in the subspace of R^3 and is spanned by the set B = {u1, u2}. Making use of the fact that the set B is orthogonal, express v in terms of B where, v = 1 -2 -13 B = 1 1 2 , 1 3 -1 v is a matrix and B is a set of 2 …
  5. Math

    Mark each of the following True or False. ___ a. All vectors in an orthogonal basis have length 1. ___ b. A square matrix is orthogonal if its column vectors are orthogonal. ___ c. If A^T is orthogonal, then A is orthogonal. ___ d. …
  6. math

    given that vectors(p+2q) and (5p-4q) are orthogonal,if vectors p and q are the unit vectors,find the product of vectors p and q?
  7. math

    given that vectors(p+2q) and (5p-4q) are orthogonal,if vectors p and q are the unit vectors,find the dot product of vectors p and q?
  8. linear algebra urgent

    For the orthogonal matrix A = 1/sqrt(2) -1/sqrt(2) -1/(sqrt(2)) -1/sqrt(2) verify that (Ax,Ay)=(x,y) for any vectors x and y in R2. Can someone please explain this
  9. linear algebra

    Hello, how can I proof the next theorem? I have a linear transformation T(X) that can be express as T(X)=AX and A is an orthogonal matrix, then ||T (X)||=||X|| , I was doing this: ||T (X)||=sqrt(<AX,AX>) But I don't know what
  10. Linear Algebra

    Hi, I really need help with these True/False questions: (a) If three vectors in R^3 are orthonormal then they form a basis in R^3. (b) If Q is square orthogonal matrix such that Q^2018 = I then Q^2017 = Q^T. (c) If B is square orthogonal …

More Similar Questions