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Question: The vector that must be added to the vector \(\widehat{i} - 3\widehat{j} + 2\widehat{k}\) and \(3\wi...

The vector that must be added to the vector i^−3j^+2k^\widehat{i} - 3\widehat{j} + 2\widehat{k} and 3i^+6j^−7k^3\widehat{i} + 6\widehat{j} - 7\widehat{k} so that the resultant vector is a unit vector along the y­­-axis is

A

4i^+2j^+5k^4\widehat{i} + 2\widehat{j} + 5\widehat{k}

B

−4i^−2j^+5k^- 4\widehat{i} - 2\widehat{j} + 5\widehat{k}

C

3i^+4j^+5k^3\widehat{i} + 4\widehat{j} + 5\widehat{k}

D

Null vector

Answer

−4i^−2j^+5k^- 4\widehat{i} - 2\widehat{j} + 5\widehat{k}

Explanation

Solution

Unit vector along y axis =j^= \widehat{j} so the required vector

=j^−[(i^−3j^+2k^)+(3i^+6j^−7k^)]=−4i^−2j^+5k^= \widehat{j} - \lbrack(\widehat{i} - 3\widehat{j} + 2\widehat{k}) + (3\widehat{i} + 6\widehat{j} - 7\widehat{k})\rbrack = - 4\widehat{i} - 2\widehat{j} + 5\widehat{k}