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Find the unit vector in the direction of (4,-4). Write your answer in component form. Do not approximate any numbers in your answer.

User Baku
by
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1 Answer

3 votes

Answer:


((1)/(√(2) ), (-1)/(√(2) ) )

Explanation:

The unit vector for a nonzero vector, say u, in the direction of u is given by:

û =
(u)/(|u|) ---------------(i)

Where;

|u| = magnitude of vector u

From the question;

u = (4, -4)

First let's calculate the magnitude of u as follows;

|u| =
√((4)^2 + (-4)^2)

|u| =
√(16 + 16)

|u| =
√(32) =
4√(2)

Now, substitute u and |u| into equation (i) as follows;

û =
((4, -4))/(4√(2) )

û =
((4)/(4√(2) ), (-4)/(4√(2) ) )

û =
((1)/(√(2) ), (-1)/(√(2) ) )

Therefore, the unit vector is
((1)/(√(2) ), (-1)/(√(2) ) )

User Taskmaster
by
8.3k points

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