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Let vec(a)= 2vec(i) + vec(k), vec(b) = v...

Let `vec(a)= 2vec(i) + vec(k), vec(b) = vec(i) + vec(j) + vec(k) and vec( c)= 4vec(i) -3vec(j) + 7vec(k)`. Determine a vector `vec(r )` satisfying `vec( r) xx vec(b)= vec( c) xx vec(b) and vec(r ).vec(a)= 0`.

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The correct Answer is:
`-7 vec(j) + 3vec(k)`
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