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    I've got a notation question. The question is to find the area of a parallelogram with sides

    \vec{a} = a_x\mathbf{i} + a_y\mathbf{j} + a_z\mathbf{k}

    \vec{a} = b_x\mathbf{i} + b_y\mathbf{j} + b_z\mathbf{k}

    I know that the area is given by \mathbf{A} = | \vec{a} \times \vec{b} |, which can be derived by breaking the parallelogram into 2 triangles and using the formula for the area of a triangle.

    I'd like to know if it is mathematically acceptable to write |\vec{a} \times \vec{b}| = \begin{Vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ a_x & a_y & a_z \\ b_x & b_y & b_z \end{Vmatrix} as a result of \vec{a} \times \vec{b} begin equal to \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ a_x & a_y & a_z \\ b_x & b_y & b_z \end{vmatrix}.

    If not, then does the double vertical line on either side of the matrix mean something else?



    I also wanted to know the meaning of the term antiparallel. Does it mean that if \vec{a} is antiparallel to \vec{b}, then \vec{a} = - \lambda\vec{b}, where \lambda > 0 ?
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    (Original post by Khallil)
    I've got a notation question. The question is to find the area of a parallelogram with sides

    \vec{a} = a_x\mathbf{i} + a_y\mathbf{j} + a_z\mathbf{k}

    \vec{a} = b_x\mathbf{i} + b_y\mathbf{j} + b_z\mathbf{k}

    I know that the area is given by \mathbf{A} = | \vec{a} \times \vec{b} |, which can be derived by breaking the parallelogram into 2 triangles and using the formula for the area of a triangle.

    I'd like to know if it is mathematically acceptable to write |\vec{a} \times \vec{b}| = \begin{Vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ a_x & a_y & a_z \\ b_x & b_y & b_z \end{Vmatrix} as a result of \vec{a} \times \vec{b} begin equal to \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ a_x & a_y & a_z \\ b_x & b_y & b_z \end{vmatrix}.

    If not, then does the double vertical line on either side of the matrix mean something else?



    I also wanted to know the meaning of the term antiparallel. Does it mean that if \vec{a} is antiparallel to \vec{b}, then \vec{a} = - \lambda\vec{b}, where \lambda > 0 ?
    Perhaps try maths stackexchange?
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    (Original post by keromedic)
    Perhaps try maths stackexchange?
    Will do!
 
 
 
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