Question

Please help

A vector is drawn on a grid

Answer 1

.....

..

...

..

Explanation:

I cant see the grid

Answer 2

The vector on the grid, from (2, 1) to (8, 5), is expressed as
`\( \mathbf{v} = 2\mathbf{a} + \mathbf{b} \)` using vector decomposition with given vectors
`\( \mathbf{a} \) and \( \mathbf{b} \).`

To express the vector drawn on the grid in terms of vectors
`\( \mathbf{a} \)` and
`\( \mathbf{b} \)`, we can utilize the given vectors
`\( \mathbf{a} = \begin{bmatrix} 1 \\ 3 \end{bmatrix} \)` and
`\( \mathbf{b} = \begin{bmatrix} 4 \\ -2 \end{bmatrix} \)`. The vector on the grid starts from (2, 1) and ends at (8, 5). The displacement between these points represents the desired vector.

The displacement vector
`\( \mathbf{v} \)` can be obtained by subtracting the initial point from the terminal point:

`\[ \mathbf{v} = \begin{bmatrix} 8 - 2 \\ 5 - 1 \end{bmatrix} = \begin{bmatrix} 6 \\ 4 \end{bmatrix} \]`

Now, to express
`\( \mathbf{v} \)` in terms of
`\( \mathbf{a} \) and \( \mathbf{b} \),` we can use vector decomposition. We want to find scalars
`\( \alpha \)` and
`\( \beta \)` such that
`\( \mathbf{v} = \alpha \mathbf{a} + \beta \mathbf{b} \).`

`\[ \begin{bmatrix} 6 \\ 4 \end{bmatrix} = \alpha \begin{bmatrix} 1 \\ 3 \end{bmatrix} + \beta \begin{bmatrix} 4 \\ -2 \end{bmatrix} \]`

Solving for
`\( \alpha \)` and
`\( \beta \),` we find
`\( \alpha = 2 \) and \( \beta = 1 \)`. Therefore, the vector
`\( \mathbf{v} \)` can be expressed as:

`\[ \mathbf{v} = 2\mathbf{a} + \mathbf{b} \]`

In conclusion, the vector drawn on the grid can be expressed as twice vector
`\( \mathbf{a} \)` plus vector
`\( \mathbf{b} \).`