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)>#.