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Triangle problem using vectors

  1. Sep 21, 2003 #1

    Dx

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    [SOLVED] triangle problem using vectors

    Hi!
    question: Two sides of a triangle are formed by vectors i - 4j-k and -2i - j+k. The area is ?

    A=1/2bh so I know to multiply the two vectors as such 1/2(vector1 x vector2) But what do I substitute foe i, j and k? Its not given in the problem.
    so far...
    1/2(-2i^2-ij+ik+8ji+4j^2-4jk+2ki+kj-k^2)
    so what do I substitute foe i, j and k?
    Dx :wink:
     
  2. jcsd
  3. Sep 21, 2003 #2
    You shouldn't concern yourself with i's and j's for an area problem. A= (1/2)(|v_1|)(|v_2|)sinO. So find the magnitudes of the vectors and find the angle between them.
     
  4. Sep 22, 2003 #3

    HallsofIvy

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    How in the world could you be doing a problem like this if you don't know what i,j, i are?

    It's not a matter of "what to substitute for i, j, k". They are not numbers. i is the unit vector in the x direction, j is the unit vector in the y direction, k is the unit vector in the z direction.

    Also, you do not multiply vectors the way you seem to be trying.

    Here, "u x v" is the cross product. It can be defined as "the vector whose length is |u||v|sin(theta) (where theta is the angle between the two vectors) and whose direction is perpendicular to both u and v in the "right hand rule" sense.

    It can also be calculated as a determinant:

    | i j k|
    | 1 -4 -1|
    |-2 -1 1|
    which equals i((-4)(1)-(-1)(-1))- j(1(1)-(-1)(-2)+ k(1(-1)-(-2)(-4))
    or -5i+ j- 9 k. It's length is [sqrt](25+ 1+ 91)= [sqrt](117)
    Half of that is the area of the triangle.
     
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