Find Unit Vector?

Question

First of all, what is, in simple words, a unit vector?

Find the unit vector having the same direction as v.

(1) v = -3j

(2) v = -5i + 12j

Answer 1

a unit vector = vector / length of vector = v / | v|

(1) v = -3j
=> v / | v|
=> -3j / | -3j |
=> -3j / 3
=> - j

(2) v = -5i + 12j
=> v / | v|
=> -5i + 12j / | -5i + 12j
=> -5i + 12j / √[ (-5)² + (12)² ]
=> -5i + 12j / √169
=> -5i + 12j / 13
=> -5i / 13+ 12j/ 13

ANS : v = v = -(5/13) i + (12/13) j

Answer 2

How To Find Unit Vector

Answer 3

This Site Might Help You.

RE:
Find Unit Vector?
First of all, what is, in simple words, a unit vector?

Find the unit vector having the same direction as v.

(1) v = -3j

(2) v = -5i + 12j

Answer 4

A unit vector is a vector with a length or magnitude equal to one.

A vector has both magnitude and direction, so a unit vector will be a vector that has the same direction as the original vector, but it's length is equal to one. You obtain this vector by dividing each vector component by its magnitude.

1. v = -j

2. The length of that vector is 13 (Pythagorean theorem).

v = -(5/13) i + (12/13) j

proof: sqrt [ (-5/13)^2 +(12/13)^2 ] = 1

Answer 5

A unit vector is just a vector with a length of one. In general if you have a vecor V and want to make it a unit vector simply divide by the magnitude of the vector: v(unit vector) = V/|V|

1. This is easy. it is just j since i, j and k are unit vectors by defintion.

2. magnitude of v = SQRT(5^2 + 12^2) = SQRT(169) = 13
So the unit vector is (-5/12)i + (12/13)j

Answer 6

I've attached a color coded PDF at the link below to illustrated example 1. The second page illustrates the procedure in general. It's formatted to look like textbook writing for easy reading.
http://www.tomsmath.com/step-by-step-directions-for-finding-a-unit-vector-along-another-vector.html