Question

Find two vectors orthogonal to the given vector.u = (4,9)

Answer 1

Explanations:

For two vectors to be orthogonal, their dot product must be zero vector. Let the required vectors be (±x, ±y).

Using the expression;

`(4,9)\cdot(\pm x,\pm y)=(0,0)`

Take the dot product

`4x+9y=0`

We now need to find suitable values of x and y satisfying this relationship (note we have one equation and two unknowns).

If x = 9

4(9) + 9y = 0

36 + 9y = 0

-9y =36

y = -4

Hence one of the vector will be (9, -4) and the other vector will be (-9, -(-4)) = (-9, 4)