1.

Find |vec(a)xxvec(b)|, if a=hat(i) -7hat(j)+7k and b=3hat(i)-2hat(j)+2hat(k).

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Solution :It is GIVEN that `a=hat(i)-7hat(j)+7hat(k) and b=3hat(i)-2HAT(j)+2hat(k)`.
`therefore vec(a)xxvec(b)=|(hat(i),hat(j),hat(k)),(1,-7,7),(3,-2,2)|=(-14+14)hat(i)-(2-21)hat(i)-(2-21)hat(k)=0hat(i)+19hat(j)+19hat(k)`.
`rArr |axxb|=SQRT(0^2+(19)^2+(19)^2)=sqrt(2xx(19)^2)=19sqrt(2)`.


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