# Given the vectors v=-2i+5j and w=3i+4i, determine

(do I just plug what is given? but how would I find the length? is there a special way to solve vectors?)

1. 1/2 v

2. w-v

3. length of w

4. the unit vector for v

Use the pythogrean theorm to find length of w, i,j are at right angles to each other. The unit vector is the vector divided by length.

## To solve the given vector problems, you'll need to manipulate the given vectors and apply some vector operations. Here's how you can find the answers:

1. To calculate 1/2 v, you can simply multiply each component of the vector v by 1/2. So, 1/2 v would be (-2/2)i + (5/2)j, which simplifies to -i + (5/2)j.

2. To find w-v, you subtract each component of vector v from the corresponding component of vector w. So, w-v would be (3-(-2))i + (4-5)j, which simplifies to 5i - 1j, or 5i - j.

3. To determine the length of a vector, you can use the Pythagorean theorem in a 2-dimensional space. The length of a vector w with components (w1, w2) is given by the formula length(w) = sqrt(w1^2 + w2^2). In this case, w = (3i + 4j), so the length of w would be length(w) = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5.

4. To find the unit vector for v, you need to divide the vector v by its length. First, calculate the length of v using the same formula as in step 3. Then, divide each component of v by the length of v to get the unit vector. So, the unit vector for v would be (-2/5)i + (5/5)j, which simplifies to -2/5i + j.

So, to summarize:

1. 1/2 v = -i + (5/2)j

2. w-v = 5i - j

3. length of w = 5

4. unit vector for v = -2/5i + j

Remember to always break down the problem into smaller steps, perform the necessary calculations, and simplify the result when needed.