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

1 Answer
Steve M
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 #bb(ul hat(i))# and #bb(ul hat(j))# in the #x#-direction and the #y#-direction respectively we have:

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

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