||v|| = 4. ||w|| = 4. The angle between v and w is 2.1 radians. Given this information, calculate ||4v+2w|| and ||1v-3w||?

Question

I thought it was as simple as plugging in v and w like this... ||4(4)+2(4)|| but that isn't the right answer so I'm lost on how to go about solving this. We haven't gone over this in class yet.

11912 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-11-12T17:31:28

# ||vecv-3vecw||=sqrt208.48~~14.44#

Recall that, #||vecx||^2=vecx*vecx.#

#:. ||1vecv-3vecw||^2=(vecv-3vecw)*(vecv-3vecw),#

#=||vecv||^2-2vecv*3vecw+||3vecw||^2,#

#=4^2-6vecv*vecw+9||vecw||^2,#

#=16-6{||vecv||*||vecw||*cos/_(vecv,vecw)}+9*4^2,#

#=16-6*4*4*cos(2.1)+144,#

#~~160-96(-0.505),#

#=160+48.48,#

#:. ||vecv-3vecw||=sqrt208.48~~14.44#

Similarly, #||4vecv+2vecw||# can be dealt with.