Given that the resultant of the vectors a = 2pi-5j and b = 6i-3pj is parallel to the vector c = 4i-5j, find a) the value of p b) the resultant of the vectors a and b?

1 Answer
Mar 24, 2018

#(a)" "p=5#

#(b)" resultant "=16hati-20hatj#

Explanation:

two vwctors #vecu," & "vecv#
are parallel if;

#vecu=lambdavecv#

so the resulat of #veca, vecb" is parallel to "vecc" "#if

#veca+vecb=lambda vecc#

we have from the question

#2phati-5hatj+6hati-3phatj=lambda(4hati-5hatj)#

equating components

#hati " components "rarr2p+6=4lambda--(1)#

#hatj" components "rarr5+3p=5lambda--(2)#

solving

#(1)xx3rarr6p+18=12lambda#

#(2)xx2rarr6p+10=10lambda#

subtract

#2lambda=8=>lambda=4#

substitute into #(1)#

#6p=12xx4-18=30#

#=>p=5#

a quick mental check in #(2) "verifies the values for "p " & " lambda#

#:.veca=2xx5hati-5hatj=10hati-5hatj#

#vecb=6hati-3xx5hatj=6hati-15hatj#

#resultant

#veca+vecb=10hati-5hat j+6hati-15hatj#

#=16hati-20hatj#