The angle θ , where 0 < θ < 180o between the vectors u & w, where u= i + 2j - k, v= 3 i - j + 4k, & w= 2j - k

possible angle...





a. 24.1o





b. 57.2o





c. 79.5o





d. 100.1o





e. 103.9o





f. 113.6o





g. 121.8o





h. 132.4o





or is it none of these?

The angle θ , where 0 %26lt; θ %26lt; 180o between the vectors u %26amp; w, where u= i + 2j - k, v= 3 i - j + 4k, %26amp; w= 2j - k
cos(theta) = u.w / ( |u| |w| )


= (1,2,-1).(0,2,-1) / sqrt(6)sqrt(5)


= (0 + 4 + 1) / sqrt(30)


theta = arccos(5/sqrt(30))


= 24.1deg.
Reply:It's about 24.1 degrees.





The vector "v" is not needed, this problem is only about u %26amp; w.





dot product of u %26amp; w = [ 1*0 + 2*2 + (-1)*(-1) ] [ |u| |w| ]


= [ 0 + 4 +1 ] / [sqrt(6)* sqrt(5) ]


= 5 / [sqrt(6)* sqrt(5) ] = sqrt(0.83333...) = 0.9128709...


arccos(0.9128709...) = 24.094843... degrees

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