||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.

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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.