Solving a vector equation [duplicate]

I want a simple and intuitive way of solving for $t$ given that $\mathbf{i},\, \mathbf{j},\, \mathbf{k}$ are the unit vectors in $\mathbf{R}^3$. $$5 = (2 \mathbf{i} - 3 \mathbf{k} + (\mathbf{i} - \mathbf{j} + \mathbf{k})\, t)\cdot(2 \mathbf{i} + 3 \mathbf{j} + 4 \mathbf{k})$$ I want to point out that I often get equations provided like this and I am not looking to solve it. I do understand that $(4-12+t\,(2-3-4))=5$ provides me with the answer 13/5. Now I am simply interested in solving this with as little as possible transformation of the expressions.

• a quick simple and intuitive way would do! – ALEXANDER May 5 '15 at 10:13

i = {1, 0, 0};

• Mathematica substitutes the (list) values for $i$, $j$, and $k$ when executing Solve. – David G. Stork May 5 '15 at 10:27
• One could also do {i, j, k} = IdentityMatrix[3];, or use UnitVector[] – J. M.'s technical difficulties May 5 '15 at 11:45