Find the component form and magnitude of a vector with the initial point P(2,-3) and Q(-6,7)

Answer 1

To find the component form of the vector with initial point P(2,-3) and terminal point Q(-6,7), we subtract the coordinates of the initial point from the coordinates of the terminal point.

Component form:
Let the vector be denoted as vector PQ. The x-component of the vector is -6 - 2 = -8, and the y-component of the vector is 7 - (-3) = 10.

Therefore, the component form of the vector PQ is (-8, 10).

Magnitude:
To find the magnitude of the vector PQ, we use the Pythagorean theorem:

Magnitude = sqrt((-8)^2 + 10^2)
Magnitude = sqrt(64 + 100)
Magnitude = sqrt(164)
Magnitude ≈ 12.81

Therefore, the magnitude of the vector PQ is approximately 12.81.