Question

Find the component form and magnitudeof A(2,4),B(-1,3)

Answer 1

The component form of the vector from A to B is (-3, -1), and the magnitude is approximately 3.1623.

Step-by-step explanation:

To find the component form of the vector connecting points A(2,4) and B(-1,3), we calculate the differences in the x and y coordinates:

• Ax = Bx - Ax = -1 - 2 = -3
• Ay = By - Ay = 3 - 4 = -1

Therefore, the component form is (-3, -1).

To find the magnitude of the vector from A to B, we apply the Pythagorean theorem:

Magnitude = √((-3)2 + (-1)2) = √(9 + 1) = √(10) ≈ 3.1623