If #A= <5 , 6 ># and #B= <-1,4 >#, what is #||A+B|| -||A|| -||B||#?

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Answer 1 · 2017-05-05T22:27:46

# ||vec(A+B) || - || vecA ||-|| vecB || = sqrt(116)-sqrt(61) -sqrt(17) #
# " " = 1.1630 (4dp) #

We have:

# vecA = <<5,6>>#

#vec B =<<-1,4>>#

So:

# vec(A+B) = <<4,10>>#

So the norms are:

# || vecA || = sqrt(5^2+6^2) #
# " " = sqrt(25+36) #
# " " = sqrt(61) #

# || vecB || = sqrt((-1)^2+4^2) #
# " " = sqrt(1+16) #
# " " = sqrt(17) #

And;

# ||vec(A+B) ||= sqrt(4^2+10^2) #
# " " = sqrt(16+100) #
# " " = sqrt(116) #

Hence:

# ||vec(A+B) || - || vecA ||-|| vecB || = sqrt(116)-sqrt(61) -sqrt(17) #
# " " = 1.1630 (4dp) #