How do you find the component form and magnitude of vector qp given the points p(5, 11) and q(6, 4)?

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To find the component form and magnitude of the vector qp given the points p(5, 11) and q(6, 4), we need to perform the following steps:

Step 1: Find the Component Form

The component form of a vector is determined by subtracting the coordinates of the initial point from the coordinates of the terminal point. In our case, we need to calculate:

 qp = (xp - xq, yp - yq)

Substituting the coordinates:

 qp = (5 - 6, 11 - 4)

So, 

 qp = (-1, 7)

Step 2: Calculate the Magnitude

The magnitude of a vector can be found using the following formula:

 |qp| = √((x2 - x1)² + (y2 - y1)²)

Applying it to our vector:

 |qp| = √((-1)² + (7)²)

This simplifies to:

 |qp| = √(1 + 49)

So, the final magnitude is:

 |qp| = √(50)

Which can be further simplified to:

 |qp| ≈ 7.07

Final Result

The component form of the vector qp is (-1, 7) and its magnitude is approximately 7.07.

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