What is the unit vector of this vector v = 2i - j + k?

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Answer 1 · 2016-12-16T18:38:21

$u=<2/sqrt(6),-1/sqrt(6), 1/sqrt(6)>$ .

To determine the unit vector, divide the given vector by its magnitude.

The magnitude of the vector is given by $sqrt((i)^2+(j)^2+(k)^2)$ , where $i, j$ , and $k$ are those components of the vector.

For $v=2i-j+k$ , equivalent to $v=<2,-1,1>$ , the magnitude is given by

$sqrt((2)^2+(-1)^2+(1)^2) = sqrt(6)$ .

Thus, the unit vector is found by

$(<2,-1,1>)/(sqrt(6))$

Equivalently, $u=<2/sqrt(6),-1/sqrt(6), 1/sqrt(6)>$ .