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2 months ago

G Find non-zero vectors x and y that are both orthogonaland orthogonal to each other.

Mathematics

1 answer:

babunello [11.8K]2 months ago

4 0

Answer:

x = <1,5>

y = <-5,1>

Step-by-step explanation:

Let x, y represent two vectors in 2D

defined as:

x = <a, b>

y = <c, d>

for x, y to be orthogonal, we understand that their dot or scalar product should equal zero, therefore

x. y = 0

<a, b>. <c, d> = 0

a*c + b*d = 0 ------ (A)

Now, select any four values for a, b, c, and d that fulfill equation (A)

for example, I choose (this is subject to personal choice):

a=1, b=5, c=-5, d=1

Verifying Equation (A):

(1)*(5) + (-5)*(1) =0

5 - 5 = 0

0 = 0 (True)

Thus,

The identified vectors x, y are:

x = <1, 5>

y = <-5, 1>

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