Given the vectors #u=<2,2>#, #v=<-3,4>#, and #w=<1,-2>#, how do you find #||w||-1#?

1 Answer
Jan 7, 2017

Answer:

# || vec w || -1 = sqrt( 5 ) - 1 = 1.24# (2dp)

Explanation:

We have:

#vec u=<<2,2>>#
#vec v=<<-3,4>>#
#vec w=<<1,-2>>#

The question does seem a little bit confused as there is no further reference to #vec u# or #vec v#!

# || vec w || = sqrt( vec w * vec w ) #
# \ \ \ \ \ \ \ \ = sqrt( (1)^2 + (-2)^2 ) #
# \ \ \ \ \ \ \ \ = sqrt( 1 + 4 ) #
# \ \ \ \ \ \ \ \ = sqrt( 5 ) #

So then

# || vec w || -1 = sqrt( 5 ) - 1 #