Question

Help with vectors

Answer 1

\[||v||~=~1 ~and ~||w||~= 3\]\[find~ = ~ ||2v+1w|| \]\[~~~~~~~~and ~||2v-3w||\]

Answer 2

@ganeshie8

Answer 3

we need more info. For example, do they say if v and w are orthogonal?

Answer 4

no but they have an angle of 0.2 in radians

Answer 5

if that helps
@phi

Answer 6

yes, that helps a lot

use these ideas:
\[ | v |^2 = v \cdot v = \\ \text{ and } |v|= \sqrt{v \cdot v} \]
also
\[ v \cdot w= |v| \ |w| \cos(angle) \]
start by expanding
\[ | 2v+w|^2 = (2v+w) \cdot (2v+w)\]

Answer 7

\[4|v|+2(v*w)+2(w*v)+|w|\]
is it good so far?

Answer 8

almost, but v dot v is |v|^2 ditto w dot w

Answer 9

and v dot w = w dot v (dot product commutes) so you can combine the two middle terms

Answer 10

4|v|^2 + 4(2(v*w)) + |w|^2
like this

Answer 11

not sure about the middle part

Answer 12

the middle is 2 v*w + 2 v*w = 4 v*w (* means dot product)

Answer 13

so you have
4|v|^2 + 4 v*w + |w|^2

now use |v|= 1
|w|= 3

v*w = |v| |w| cos(0.2 radians)

to get a number
finally, take the square root for the answer.

Answer 14

okay i got it
Thanks Alot

Answer 15

what did you get?

Answer 16

sqrt(4+4*(3cos(0.2))+(3^2)) = 4.97602

Answer 17

yes