# How do you find the magnitude of #<-10,-5># and write it as a sum of the unit vectors?

##### 1 Answer

Oct 23, 2017

# abs( << -10, -5 >> ) = 5sqrt(5)#

# << -10, -5 >> = -10bb(ul hat(i)) - 5bb(ul hat(j)) #

#### Explanation:

The magnitude is given by the metric norm:

# abs( << -10, -5 >> ) = sqrt((-10)^2+(-5)^2)#

# " " = sqrt(100+25)#

# " " = sqrt(125)#

# " " = 5sqrt(5)#

And using standard unit vector

# << -10, -5 >> = -10bb(ul hat(i)) - 5bb(ul hat(j)) #