How do you find a unit vector in the direction of 3i+4j-k?

Question

54728 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-18T08:53:47

#(3 i + 4 j - k) / (sqrt(26))#

We have: #3 i + 4 j - k#

Let #u = 3 i + 4 j - k#.

Unit vectors are of the form #hat(u) = (u) / (abs(u))#:

#=> hat(u) = (3 i + 4 j - k) / (abs(3 i + 4 j - k))#

#=> hat(u) = (3 i + 4 j - k) / (sqrt(3^(2) + 4^(2) + (- 1)^(2)))#

#=> hat(u) = (3 i + 4 j - k) / (sqrt(9 + 16 + 1))#

#=> hat(u) = (3 i + 4 j - k) / (sqrt(26))#