Now, Now,We are given the following vectors:
We are asked to determine the following vector:
First, we will determine the vector PQ and RS. To determine PQ we use the following:
This means we need to subtract "P" from "Q". We do that by subtracting each component of the points, like this:
Solving the operations:
Now, we use a similar procedure to determine RS:
Substituting we get:
Solving the operations:
Now, we substitute the values in the vector we are looking for:
Now, we solve the product by multiplying both components of RS:
Now, we solve the addition by adding each corresponding component:
Solving the operations:
And thus we have determined the components.
Part B. We area asked to determine the magnitude of the vector. To do that we will use the following:
Given a vector of the form:
Its magnitude is:
This means that the magnitude is the square root of the sum of the square of the components. Applying the formula we get:
Now, we solve the squares:
Solving the addition:
Now, we factor the term inside the radical as follows:
Now, we distribute the radical:
Taking the left square root:
And thus we have determined the magnitude.