Q75 / 160 · TS EAMCET 2006 · Mathematics

The position vector of a point lying on the line joining the points whose positions vectors are $\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$ is :

  • A
    $\hat{\mathbf{j}}$
  • Correct answer
    B
    $\hat{\mathbf{i}}$
  • C
    $\hat{\mathbf{k}}$
  • D
    $\overrightarrow{\mathbf{0}}$

Solution

The position vector of mid point of line joining the points whose position vector are $\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$. $=\frac{\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}+\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}}{2}=\frac{2 \hat{\mathbf{i}}}{2}=\hat{\mathbf{i}}$

Hence, the correct answer is option: 'B'.

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