Solveeit Logo
Login

Question

Question: What should be added in vector $\bar{a}=3\hat{i}+4\hat{j}-2\hat{k}$ to get its resultant a vector $\...

What should be added in vector aˉ=3i^+4j^−2k^\bar{a}=3\hat{i}+4\hat{j}-2\hat{k} to get its resultant a vector i^\hat{i}?

A

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

B

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

C

2i^+4j^−2k^2\hat{i}+4\hat{j}-2\hat{k}

D

None of these

Answer

-2\hat{i}-4\hat{j}+2\hat{k}

Explanation

Solution

Let the vector to be added be xˉ\bar{x}. Then aˉ+xˉ=i^\bar{a} + \bar{x} = \hat{i}. Therefore, xˉ=i^−aˉ=i^−(3i^+4j^−2k^)=−2i^−4j^+2k^\bar{x} = \hat{i} - \bar{a} = \hat{i} - (3\hat{i}+4\hat{j}-2\hat{k}) = -2\hat{i}-4\hat{j}+2\hat{k}.