Question

Find the component form and the magnitude of the vector v. initial point (-5, 9) terminal point (16, -63)?

Answer 1

The component form of the vector v with initial point (-5, 9) and terminal point (16, -63) is v = <21, -72>, and its magnitude is 75.

Step-by-step explanation:

To find the component form of the vector v with the given initial point (-5, 9) and terminal point (16, -63), we subtract the coordinates of the initial point from the corresponding coordinates of the terminal point:

• Vx = 16 - (-5) = 21
• Vy = -63 - 9 = -72

So, the component form of vector v is v = <21, -72>.

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

v = √(Vx² + Vy²) = √(21² + (-72)²) = √(441 + 5184) = √5625 = 75

The magnitude of vector v is 75.