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Find vec(a)xxvec(b) and vec(b)xxvec(a) i...

Find `vec(a)xxvec(b)` and `vec(b)xxvec(a)` if
(i) `vec(a)=3hat(k)+4hat(j), vec(b)=hat(i) +hat(j)-hat(k)`
`vec(a)=(2, -1,1) ,vec(b)=(3,4, -1)`

Text Solution

Verified by Experts

(i) `vec(a)xxvec(b)=|(hat(i),hat(j),hat(k)),(0, 4, 3),(1,1,-1)|=-7hat(i)+3hat(j)-4hat(k)`
`vec(b)xxvec(a)=|(hat(i),hat(j),hat(k)),(1, 1, -1),(0,4,3)|=7hat(i)3hat(j)+4hat(k)`
Thus `vec(a)xx vec(b) != vec(b)xxvec(a)`
(ii) `vec(a)xxvec(b)=|(hat(i),hat(j),hat(k)),(2, -1, 1),(3,4,-1)|= -3hat(i)+5hat(j)+11hat(k)`
`vec(b)xxvec(a)=|(hat(i),hat(j),hat(k)),( 2, -1, 1),(3, 4, -1)|=3hat(i)-5hat(j)-11hat(k)`
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