Question

Чему равны координаты вектора p=3q+2r-z, если вектор q=(1;0;2);вектор r=(2;1;-1);вектор z=(2;0;1)

Answer 1

P=(1*3;0;2*3)+(2*2;2;-2)-z
P=(4+4;2;6-2)-z
P=(8-2;2;4-1);
P=(6;2;3);

Answer 2

I can help you with your math question. To find the coordinates of the vector p=3q+2r-z, you need to perform the following steps:

- Write the coordinates of each vector as a column matrix: $$q=\begin{pmatrix}1\\0\\2\end{pmatrix}, r=\begin{pmatrix}2\\1\\-1\end{pmatrix}, z=\begin{pmatrix}2\\0\\1\end{pmatrix}$$ - Multiply each vector by the corresponding scalar: $$3q=\begin{pmatrix}3\\0\\6\end{pmatrix}, 2r=\begin{pmatrix}4\\2\\-2\end{pmatrix}, -z=\begin{pmatrix}-2\\0\\-1\end{pmatrix}$$ - Add the resulting vectors: $$p=3q+2r-z=\begin{pmatrix}3\\0\\6\end{pmatrix}+\begin{pmatrix}4\\2\\-2\end{pmatrix}+\begin{pmatrix}-2\\0\\-1\end{pmatrix}=\begin{pmatrix}5\\2\\3\end{pmatrix}$$ - Write the coordinates of the vector p as a tuple: $$p=(5;2;3)$$

Therefore, the coordinates of the vector p are (5;2;3). You can learn more about vectors and their operations from [this website](https://ru.onlinemschool.com/math/assistance/vector/p_to_vector/) or [this one](https://skysmart.ru/articles/mathematic/vektor). I hope this helps.