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Question: What vector must be added to the two vectors \(\widehat{i} - 2\widehat{j} + 2\widehat{k}\) and \(2\w...

What vector must be added to the two vectors i^−2j^+2k^\widehat{i} - 2\widehat{j} + 2\widehat{k} and 2i^+j^−k^,2\widehat{i} + \widehat{j} - \widehat{k}, so that the resultant may be a unit vector along x-axis

A

2i^+j^−k^2\widehat{i} + \widehat{j} - \widehat{k}

B

−2i^+j^−k^- 2\widehat{i} + \widehat{j} - \widehat{k}

C

2i^−j^+k^2\widehat{i} - \widehat{j} + \widehat{k}

D

−2i^−j^−k^- 2\widehat{i} - \widehat{j} - \widehat{k}

Answer

−2i^+j^−k^- 2\widehat{i} + \widehat{j} - \widehat{k}

Explanation

Solution

(i^−2j^+2k^)+(2i^+j^−k^)+R→=i(\widehat{i} - 2\widehat{j} + 2\widehat{k}) + (2\widehat{i} + \widehat{j} - \widehat{k}) + \overrightarrow{R} = i

∴ Required vector R→\overrightarrow{R}= −2i^+j^−k^- 2\widehat{i} + \widehat{j} - \widehat{k}