Question

Determine whether the vectors u and v are parallel, orthogonal, or neither. u = <10, 0>, v = <0, -9>

Answer 1

Answer:

The vectors u and v are orthogonal

Step-by-step explanation:

* Lets explain Parallel and Perpendicular Vectors

- Two vectors A and B are parallel if and only if A = k B , k is a constant

  not equal to zero.

- Two vectors A and B are perpendicular if and only if their scalar

  product is equal to zero.

* Lets solve the problem

- Vector u = <10 , 0>

- Vector v = <0 , - 9>

∵ 10 ≠ k(0) and 0 ≠ k(-9)

∴ u ≠ k . v

∴ The vectors u and v are not parallel

∵ The scalar product of the vectors <a , b> and <c , d> is

   ac + bd

∵ The scalar product of u and v = 10(0) + 0(-9) = 0 + 0 = 0

∴ The vectors u and v are orthogonal