Question

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 = < , >, and ||u|| ≈ units.

Answer 1

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

Step-by-step explanation:

The question is asking to find the component form of a vector u with an initial point at (14, -6) and a terminal point at (-4, 7), and then to calculate its magnitude rounded to the nearest tenth. To find the component form, subtract the coordinates of the initial point from the coordinates of the terminal point. The component form of vector u is u = < -18, 13 >.

Next, to find the magnitude of vector u, we use the Pythagorean theorem: ||u|| = √((-18)2 + (13)2). This gives us ||u|| = √(324 + 169) = √493, which is approximately 22.2 when rounded to the nearest tenth.

Therefore, the component form of u is < -18, 13 >, and its magnitude is ||u|| ≈ 22.2 units.