Saved Bookmarks
| 1. |
Find the sine of the angle between the vectors `vec(a) =(2 hat(i) - hat(j) + 3 hat(k)) and vec(b) = (hat(i) + 3 hat(j) + 2 hat(k)).` |
|
Answer» We have `(vec(a) xxvec(b))= |(hat(i),hat(j),hat(k)),(2,-1,3),(1,3,2)|` `= (-2 -9) hat(i) - (4-3)hat(j) + ( 6+1)hat(k)` `=(-11hat(i) - hat(j) + 7 hat(k)).` `|vec(a) xx vec(b)|=sqrt((-11)^(2)+ (-1)^(2) + 7^(2))=sqrt(171) = 3 sqrt(19)` `|vec(a)|= sqrt(2^(2)+ (-1)^(2)+ 3^(2))=sqrt(14) ,` `|vec(b)|=sqrt(1^(2)+3^(2) + 2^(2)) =sqrt(14).` Let`theta" be the angle between "vec(a) and vec(b).` Then, `sin theta =(|vec(a) xx vec(b)|)/(|vec(a)| |vec(b)|) =(3sqrt(19))/((sqrt(14)) (sqrt14))=3/14 sqrt(19).` |
|