The vector equation of the line passing throu | vedclass

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Question

(A) The line passes through the point with position vector $\vec{a} = 2 \hat{i} + \hat{j} - 3 \hat{k}$.Since the line is perpendicular to the vectors

Vedclass · Accepted Answer

$\bar{r}=(2 \hat{i}+\hat{j}-3 \hat{k})+\lambda(-3 \hat{i}+2 \hat{j}+\hat{k})$

Vedclass · Answer

(A) The line passes through the point with position vector $\vec{a} = 2 \hat{i} + \hat{j} - 3 \hat{k}$.Since the line is perpendicular to the vectors $\vec{b}_1 = \hat{i} + \hat{j} + \hat{k}$ and $\vec{b}_2 = \hat{i} + 2 \hat{j} - \hat{k}$,its direction vector $\vec{v}$ is given by the cross product $\vec{b}_1 	imes \vec{b}_2$.$\vec{v} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 1 & 1 & 1 \ 1 & 2 & -1 \end{vmatrix} = \hat{i}(-1 - 2) - \hat{j}(-1 - 1) + \hat{k}(2 - 1) = -3 \hat{i} + 2 \hat{j} + \hat{k}$.The vector equation of the line is $\vec{r} = \vec{a} + \lambda \vec{v}$.Substituting the values,we get $\vec{r} = (2 \hat{i} + \hat{j} - 3 \hat{k}) + \lambda(-3 \hat{i} + 2 \hat{j} + \hat{k})$.

The vector equation of the line passing through the point having position vector $2 \hat{i}+\hat{j}-3 \hat{k}$ and perpendicular to vectors $\hat{i}+\hat{j}+\hat{k}$ and $\hat{i}+2 \hat{j}-\hat{k}$ is

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