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Math Help - NEED HINTS ON THOSE PROBLEM--VECTOR

  1. #1
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    NEED HINTS ON THOSE PROBLEM--VECTOR

    MIDTERM IS COMING..

    NEED SOME GENERAL EXAMPLE OF SOME PROBLEM.

    HELP APPRECIATED

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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by yzc717 View Post
    MIDTERM IS COMING..

    NEED SOME GENERAL EXAMPLE OF SOME PROBLEM.

    HELP APPRECIATED

    Hint for 1:

    the vector parallel to the vector a is a constant times the vector a. a vector perpendicular to a is one for which its dot product with a is zero

    you want these two vectors to add and give you b, you will have to solve for some unknowns



    Hint for 2: if the plane is parallel, it has the same normal vector, namely <1,3,-5>.

    a plane with normal vector \vec n = <a,b,c> passing through a point (x_0,y_0,z_0) is given by

    a(x - x_0) + b(y - y_0) + c(z - z_0) = 0

    the distance, D, from a point (x_0,y_0,z_0) to a plane ax + bx + cz + d = 0 is given by:

    D = \frac {ax_0 + by_0 + cz_0 + d}{\sqrt{a^2 + b^2 + c^2}}



    Hint for 3: find c, let c = <c_1,c_2,c_3> and take its dot product with b and find the vector when you subtract it from a, set the two vectors equal and solve for the components



    Hint for 4: do the computation and set it equal zero. you should be able to see if this describes a line or not.

    then set the same computation to a nonzero constant, show that you can't get a line



    Hint for 5: come on, finding determinants is something you can look up, quite easily. google is your friend.



    Hint for 6: again, something you can look up.
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  3. #3
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    can anyone show me the solution for problem1 and 3?
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