Find the angle between two vectors, 10 and 15 units long, when their resultant is (a) 20 units long and (b) 12 units long. Draw the appropriate figure?

1 Answer
ali ergin
Dec 30, 2017

#"please see the solution below."#

Explanation:

#"you can use the cosine theorem to solve this problem."#
#c^2=a^2+b^2+2*a*b*cos theta#
#"where;"#

#a)#

enter image source here

#c=20#
#a=10#
#b=15#
#20^2=10^2+15^2+2*10*15*cos theta#
#400=100+225+300*cos theta#
#400=325+300*cos theta#
#400-325=300*cos theta#
#75=300*cos theta#
#cos theta=75/300=1/4#
#theta =75.52 " deg"#

#b)#

#a=10#
#b=15#
#c=12#

enter image source here

#12^2=10^2+15^2+2*10*15*cos theta#
#144=100+225+300*cos theta#
#144=325+300*cos theta#
#144-325=300*cos theta#
#-181=300*cos theta#

#cos theta=-181/300#

#theta=127.11#

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