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

Find two vectors orthogonal to the given vector.u = (4,9)-example-1
User Ddjikic
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1 Answer

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29 votes

Answer:

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)

User David Weber
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