The point having position vector vec{p} = 4ha | vedclass

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(D) point $\vec{p}$ lies on the line $\vec{r} = \vec{a} + \lambda\vec{b}$ if $\vec{p} - \vec{a}$ is parallel to $\vec{b}$, i.e., $\vec{p} - \vec{a} =

Vedclass · Accepted Answer

$\vec{r} = (6\hat{i} - 4\hat{j} + 5\hat{k}) + \lambda(2\hat{i} + 7\hat{j} + 3\hat{k})$

Vedclass · Answer

(D) point $\vec{p}$ lies on the line $\vec{r} = \vec{a} + \lambda\vec{b}$ if $\vec{p} - \vec{a}$ is parallel to $\vec{b}$, i.e., $\vec{p} - \vec{a} = k\vec{b}$ for some scalar $k$.Given $\vec{p} = 4\hat{i} - 11\hat{j} + 2\hat{k}$ and $\vec{a} = 6\hat{i} - 4\hat{j} + 5\hat{k}$.$\vec{p} - \vec{a} = (4-6)\hat{i} + (-11 - (-4))\hat{j} + (2-5)\hat{k} = -2\hat{i} - 7\hat{j} - 3\hat{k}$.For option $(D)$, $\vec{b} = 2\hat{i} + 7\hat{j} + 3\hat{k}$.Since $\vec{p} - \vec{a} = -1(2\hat{i} + 7\hat{j} + 3\hat{k}) = -1\vec{b}$, the vector $\vec{p} - \vec{a}$ is parallel to $\vec{b}$.Thus, the point lies on the line given in option $(D)$.

The point having position vector $\vec{p} = 4\hat{i} - 11\hat{j} + 2\hat{k}$ lies on which of the following lines?

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