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Question: What should be added in vector \(\mathbf{a} = 3\mathbf{i} + 4\mathbf{j} - 2\mathbf{k}\) to get its r...

What should be added in vector a=3i+4j−2k\mathbf{a} = 3\mathbf{i} + 4\mathbf{j} - 2\mathbf{k} to get its resultant a unit vector i

A

−⥂2i−4j+2k- ⥂ 2\mathbf{i} - 4\mathbf{j} + 2\mathbf{k}

B

−2i+4j−2k- 2\mathbf{i} + 4\mathbf{j} - 2\mathbf{k}

C

2i+4j−2k2\mathbf{i} + 4\mathbf{j} - 2\mathbf{k}

D

None of these

Answer

−⥂2i−4j+2k- ⥂ 2\mathbf{i} - 4\mathbf{j} + 2\mathbf{k}

Explanation

Solution

Let b\mathbf{b} should be added, then a+b=i\mathbf{a} + \mathbf{b} = \mathbf{i}

⇒b=i−a=i−(3i+4j−2k)=−2i−4j+2k.\Rightarrow \mathbf{b} = \mathbf{i} - \mathbf{a} = \mathbf{i} - (3\mathbf{i} + 4\mathbf{j} - 2\mathbf{k}) = - 2\mathbf{i} - 4\mathbf{j} + 2\mathbf{k}.