Question

Найти векторное произведение векторов а(-1;2;-3) и b(0;-4;1). Только ответ.

Answer 1

Результат векторного произведение - вектор, в нашем случае обозначен как с.
p.s. решалось с помощью матрицы.
$[ab]=(2-12)i-(-1-0)j+(4-0)k=-10i+1j+4k\\ c(-10;1;4)$

Answer 2

Finding the Cross Product of Vectors

To find the cross product of vectors \( \mathbf{a}(-1, 2, -3) \) and \( \mathbf{b}(0, -4, 1) \), we can use the formula for the cross product of two vectors in 3D space.

The cross product of two vectors \( \mathbf{u} \) and \( \mathbf{v} \) is given by: \[ \mathbf{u} \times \mathbf{v} = \begin{pmatrix} u_2v_3 - u_3v_2 \\ u_3v_1 - u_1v_3 \\ u_1v_2 - u_2v_1 \end{pmatrix} \]

Using this formula, we can calculate the cross product of vectors \( \mathbf{a} \) and \( \mathbf{b} \): \[ \mathbf{a} \times \mathbf{b} = \begin{pmatrix} -1 \\ 2 \\ -3 \end{pmatrix} \times \begin{pmatrix} 0 \\ -4 \\ 1 \end{pmatrix} \]

Now, let's calculate the cross product.