Question

What is the angle between `<7 , 3 , 1 >` and `< 8 , -9 , 8 >`?

Answer 1

`theta =70.54^0(2dp)`

Explanation:

Let `vecu =<7,3,1> and vecv =<8, -9,8>`
We know the angle between two vectors as `costheta=(vecu.vecv)/(||vecu||.||vecv||)`Now `vecu.vecv= (7*8)+(3* -9)+ (1.8)=37 ; ||vecu||=sqrt(7^2+3^2+1^2)=sqrt59; ||vecv||=sqrt(8^2+(-9)^2+8^2)=sqrt209; :.cos theta= 37/sqrt(59*209)=37/sqrt 12331=0.3331:. theta = cos^-1(0.3331)=70.54^0(2dp)`[Ans]