If `vec(a)=(4hat(i)+ 5 hat(j) - hat(k)),vec(b)=(hat(i)-4 hat(j)+ 5 hat(k))`, and`vec(c)=(3 hat(i)+ hat(j)-hat(k))` find a vector `vec(d)` which is perpendicular to both `vec(a)` and `vec(b)` and for which `vec(c )*vec(d)=21.`

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Correct Answer - `vec(d)=7(hat(i)-hat(j)-hat(k))`

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