Question

Type the correct answer in each box, Round the vector's magnitude to the nearest tenth.

Vector u has its initial point at (14, -6) and its terminal point at (-4, 7). Write the component form of u and find its magnitude.
u = <__k, __>, and |u| = __ units.

Answer 1

The component form of vector u is <-18, 13>, and its magnitude, rounded to the nearest tenth, is 22.2 units.

Step-by-step explanation:

To find the component form of vector u with an initial point at (14, -6) and a terminal point at (-4, 7), we subtract the coordinates of the initial point from the coordinates of the terminal point. Thus, the x-component of u is -4 - 14 = -18, and the y-component is 7 - (-6) = 13. So the component form of u is <-18, 13>.

To find the magnitude of vector u, we use the Pythagorean theorem: |u| = √((-18)^2 + (13)^2), which simplifies to |u| = √(324 + 169) = √493. The magnitude of vector u is approximately 22.2 units when rounded to the nearest tenth.