How do you normalize (2i+j+2k) ?

1 Answer
David G.
Jan 31, 2016

The normalized vector is (2/3i+1/3j+2/3k).

This is a unit vector in the same direction as the original vector.

Explanation:

Normalizing a vector involves dividing the coefficient of each of its elements by the length of the vector, to yield a unit vector (length =1) in the same direction as the original vector.

To do this we first need to find the length of the vector. If the vector is in the form (ai+bj+ck) then its length is given by:

l=sqrt(a^2 + b^2+c^2)

In this case this is:

l=sqrt(2^2 + 1^2+2^2) = sqrt(4+1+4) = sqrt9=3

Now we divide a, b and c by l, which is 3:

The normalized vector is (2/3i+1/3j+2/3k).

This is a unit vector in the same direction as the original vector.

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