To find the component form of the vector QP, we first need to determine the coordinates of the vector. The vector QP is obtained by subtracting the coordinates of point P from those of point Q.
The coordinates of point Q are (6, 4) and the coordinates of point P are (5, 11).
So, the component form of the vector QP is:
- QP = Q – P
- QP = (6 – 5, 4 – 11)
- QP = (1, -7)
This means the vector QP can be represented as (1, -7).
Next, we need to find the magnitude of the vector QP. The magnitude of a vector (a, b) can be found using the formula:
|QP| = √(a² + b²)
For our vector QP = (1, -7):
- |QP| = √(1² + (-7)²)
- |QP| = √(1 + 49)
- |QP| = √50
- |QP| = 5√2
Thus, the magnitude of vector QP is 5√2.