Question

Find the quantity if v = 5i - 7j and w = 3i + 2j.
a) ||v||+||w||
b) ||v||-||w||

Answer 1

We wish to find the value of
||v+w||

if v=5i-7j and w=3i+2j
........_______
|r| =../r.+..r
.....√...1....2

if r = r(1)i +r(2)j

We first find the value of

v+ w by adding v(1) +w(1) = 5+3 = 8
and by adding v(2) +w(2) = -7+2 = -5

so v+w = 8i -5j

and
.............______
|v+w| = √8²+(-5)²
...._______
=√64 + 25
....___
=√89

Answer 2

||v|| = \[\sqrt{5^{2}+(-7^{2}})\]
||w|| = \[\sqrt{3^{2}+2^{2}}\]

Answer 3

no no no \[||v+w||\neq||v||+||w||\]

Answer 4

\[||v|| = \sqrt{74}\]
\[||w||=\sqrt{13}\]

Answer 5

so does that mean that \[||v||+||w|| = \sqrt{74}+\sqrt{13}\]

Answer 6

and
\[||v||-||w|| = \sqrt{74}-\sqrt{13}\]

Answer 7

That's it. Good work. Why do you doubt?

Answer 8

well, I'm not sure if I should or can simplify further, is that answer acceptable?

Answer 9

Fine. Not anywhere else to go with it.

Answer 10

perfect! Thank you!