If #A= <3, -1 ># and #B= <-8, 6>#, what is #||A+B|| -||A|| -||B||#?

Answer 1

We find the length of the resultant vector from adding two vectors together and then subtract from it the length of the two component vectors.

#||A+B||-||A||-||B||=7.07-3.16-10=-6.09#

We are effectively finding the length of the new vectors that is the sum of two vectors, minus the lengths of each of the component vectors.

If you draw a diagram you will see why we expect the answer to be negative: the resultant vector is shorter than the two vectors that make it up (unless those two vectors are in the same direction).

First step is to add the vectors:

#A+B = <3,-1>#+#<-8,6> = <-5,5>#
Second is to find the lengths of each of the three vectors we're interested in: #A, B# and #A+B#.
#||A||=sqrt(3^2+(-1)^2)=sqrt10=3.16#
#||B||=sqrt((-8)^2+6^2)=sqrt100=10#
#||A+B||=sqrt((-5)^2+5^2)=sqrt50=7.07#

Pulling it all together,

#||A+B||-||A||-||B||=7.07-3.16-10=-6.09#

As we predicted, the answer is negative.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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