A non-zero vector v in R^2 that is orthogonal to vector u=(1,2) is
Answers
Answer:
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Answer:
v = -2i + j
Step-by-step explanation:
Given :- Vector u = ( 1, 2 ) and vector u and v are orthogonal.
To Find :- A non-zero vector v.
Solution :-
Let the vector V = xi + yj.
It is given that vector U = i + 2j.
The two vectors are orthogonal if there dot product is 0.
We can say that the vector v and u are orthogonal if u . v = 0.
So, let's apply the above logic to out given values.
V . U = 0
⇒ ( xi + yj ) . (i + 2j) = 0
⇒ x + 2y = 0
⇒ x = - 2y.
∴ x = - 2 for y = 1 or x = - 4 for y = 2 or x = - 6 for y = 3.
Therefore, the vector v can be -2i + j or - 4i + 2j or many more.
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