Question

Use the graph to answer the question.Which statement matches the vector operation shown on the coordinate grid?

Answer 1

We have the correct statement about the vectors in the graph.

We can already see that it is a sum of vectors like:

`v+w=u`

As v has starting point at (-1,0) and ending point at (3,3), we can describe the vector as:

`v=(3-(-1))\hat{i}+(3-0)\hat{j}=4\hat{i}+3\hat{j}`

As w starts at (3, 3) and ends on (5, 2), we can describe it as:w

`w=(5-3)\hat{i}+(2-3)\hat{j}=2\hat{i}-1\hat{j}`

Finally, u starts at (-1,0) and ends at (5,2), so it can be described as:

`u=(5-(-1))\hat{i}+(2-0)\hat{j}=6\hat{i}+2\hat{j}`

Answer: v + w = u for v = 4i + 3j, u = 2i - j and u = 6i + 2j [Option C].