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Find a vector vec(b) such that vec(a) xx...

Find a vector `vec(b)` such that `vec(a) xx vec(b) = vec(c)` and `vec(a).vec(b) = 3`, where `vec(a) = hat(i) + hat(j) + hat(k), vec(c) = hat(j) - hat(k)`.

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The correct Answer is:
`(5)/(3)hat(i) + (2)/(3)hat(j) + (2)/(3)hat(k)`
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Find a vector vec(b) such that vec(a)xxvec(b)=vec(c) and vec(a)*vec(b)=3 where vec(a)=hat(i)+hat(j)+hat(k),vec(c)=hat(j)-hat(k) .

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Write the direction ratio's of the vector 3vec(a) + 2vec(b) where vec(a) = hat(i) + hat(j) - 2hat(k) and vec(b) = 2hat(i) - 4hat(j) + 5hat(k) .

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Find ]vec(a)vec(b)vec(c)] , when vec(a) = 2hat(i) - 3hat(j) + 4hat(k) , vec(b) = hat(i) + 2hat(j) - hat(k) and vec(c) = 3hat(i) - hat(j) + 2hat(k) .

Find vec(a).(vec(b) xx vec(c)) , if vec(a) = 2hat(i) + hat(j) + 3hat(k), vec(b) = -hat(i) + 2hat(j) + hat(k) and vec(c) = 3hat(i) + hat(j) + 2hat(k) .

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