Question

How do you find the component form and the magnitude of the vector v given initial point (1, 3) and terminal point (- 8, - 9)?

Answer 1

The component form of vector v with initial point (1, 3) and terminal point (-8, -9) is <-9, -12>, and its magnitude is 15. This is found by subtracting the coordinates of the initial point from the terminal point and applying the Pythagorean theorem.

Step-by-step explanation:

To find the component form of vector v given the initial point (1, 3) and the terminal point (-8, -9), we subtract the coordinates of the initial point from those of the terminal point. The component form of vector v is found as follows:

• x-component: -8 - 1 = -9
• y-component: -9 - 3 = -12

Therefore, the component form of vector v is <-9, -12>.

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

Magnitude = √((-9)² + (-12)²) = √(81 + 144) = √225 = 15.

The magnitude of vector v is 15.