Question

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

Answer 1

x = <1,5>

y = <-5,1>

Explanation:

Let x, y be two vectors in 2D

defined as:

x = <a, b>

y = <c, d>

for x, y to be orthogonal, we know that their dot or scalar product must be zero so,

x . y = 0

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

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

Now, consider any four values for a, b, c, and d respectively which satisfy the equation (A)

i.e. I chose (you can choose on your own choice):

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

Verifying Equation (A):

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

5 - 5 = 0

0 = 0 (True)

Therefore,

Our vectors x, y are:

x = <1, 5>

y = <-5, 1>