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Question

Given that the non-zero vectors a and b are non-parallel and that
3a+t(2a-3b) = a+b+s(a+2b),
find the value of t and of s

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Answer 1 · 2018-03-19T11:50:21

#s = 4/7, t = -5/7#

If #vec a, vec b# are non parallel then from

#3 vec a+t(2 vec a-3vec b) = vec a+vec b+s(vec a+2 vec b)#

we conclude

#(2 +2t-s)vec a -(3t+1+2s) vec b = vec 0#

and then

#{(2 +2t-s=0),(3t+1+2s=0):}#

and solving gives

#s = 4/7, t = -5/7#