Show that the vectors # 4 bb ul a - 8bb ul b# and #-26bb ul a+52bb ul b # are parallel?

1 Answer
Dec 28, 2017

Answer:

# bb ul u# and #bb ul v# are parallel.

Explanation:

Let us assume that the vectors #bb ul u# and #bb ul v# are parallel then there exists #lamda in RR# such that:

# bb ul u = lamda bb ul v#

And using the definitions of #bb ul u# and #bb ul v# we have:

# 4 bb ul a - 8bb ul b = lamda(-26bb ul a+52bb ul b) #
# 4 bb ul a - 8bb ul b = -26lamdabb ul a+52lamdabb ul b #

Equating coefficients of #bb ul a# and #bb ul b#

# 4 \ \ \ = -26 lamda => lamda =- 2/13#
# -8 = 52 lamda \ \ \ \ => lamda = -2/13#

Hence we have found a suitable #lamda = -2/13in RR# such that

# bb ul u = lamda bb ul v#

Hence # bb ul u# and #bb ul v# are parallel.