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(A) Let the position vectors of the two points be $\bar{b} = \hat{i} + 2\hat{j} + 2\hat{k}$ and $\bar{c} = -\hat{i} + 4\hat{j} + \hat{k}$.The directio

Vedclass · Accepted Answer

$\bar{r} = (2\hat{i} - \hat{j} + \hat{k}) + \lambda(-2\hat{i} + 2\hat{j} - \hat{k})$

Vedclass · Answer

(A) Let the position vectors of the two points be $\bar{b} = \hat{i} + 2\hat{j} + 2\hat{k}$ and $\bar{c} = -\hat{i} + 4\hat{j} + \hat{k}$.The direction vector of the line joining these points is $\bar{v} = \bar{c} - \bar{b} = (-\hat{i} - \hat{i}) + (4\hat{j} - 2\hat{j}) + (\hat{k} - 2\hat{k}) = -2\hat{i} + 2\hat{j} - \hat{k}$.The equation of a line passing through point $\bar{a} = 2\hat{i} - \hat{j} + \hat{k}$ and parallel to vector $\bar{v}$ is given by $\bar{r} = \bar{a} + \lambda\bar{v}$.Substituting the values,we get $\bar{r} = (2\hat{i} - \hat{j} + \hat{k}) + \lambda(-2\hat{i} + 2\hat{j} - \hat{k})$.

The equation of a line passing through the point $(2, -1, 1)$ and parallel to the line joining the points $\hat{i} + 2\hat{j} + 2\hat{k}$ and $-\hat{i} + 4\hat{j} + \hat{k}$ is

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