Home > Trigonometry > Products, Sums, Linear Combinations, and Applications

If #A= <2 -5 ># and #B= <9, 4 >#, what is #||A+B|| -||A|| -||B||#?

Answer 1

Madelyn Adams

The answer is #=sqrt122-sqrt29-sqrt97=-4.2#

#vecA=〈2,-5〉#

#vecB=〈9,4〉#

The modulus of the vector #∥〈a,b〉∥=sqrt(a^2+b^2)#

#vecA+vecB=〈2,-5〉+〈9,4〉=〈11,-1〉#

The modulus of #vecA=∥〈2,-5〉∥=sqrt(4+25)=sqrt29#

The modulus of #vecB=∥〈9,4〉∥=sqrt(81+16)=sqrt97#

The modulus of #vecA+vecB=∥〈11,-1〉∥=sqrt(121+1)=sqrt122#

So, # ∥vecA+vecB∥-∥vecA∥-∥vecB∥=sqrt122-sqrt29-sqrt97#

#=-4.2#

By signing up, you agree to our Terms of Service and Privacy Policy

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.

If #A= &lt;2 -5 &gt;# and #B= &lt;9, 4 &gt;#, what is #||A+B|| -||A|| -||B||#?

If #A= <2 -5 ># and #B= <9, 4 >#, what is #||A+B|| -||A|| -||B||#?