Find the vector equation for the line passing | vedclass

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Question

(A) Let $\vec{a}$ and $\vec{b}$ be the position vectors of the points $A(-1, 0, 2)$ and $B(3, 4, 6)$.Then,$\vec{a} = -\hat{i} + 2\hat{k}$ and $\vec{b}

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Let $\vec{a}$ and $\vec{b}$ be the position vectors of the points $A(-1, 0, 2)$ and $B(3, 4, 6)$.Then,$\vec{a} = -\hat{i} + 2\hat{k}$ and $\vec{b} = 3\hat{i} + 4\hat{j} + 6\hat{k}$.The direction vector of the line is given by $\vec{b} - \vec{a} = (3 - (-1))\hat{i} + (4 - 0)\hat{j} + (6 - 2)\hat{k} = 4\hat{i} + 4\hat{j} + 4\hat{k}$.The vector equation of a line passing through points with position vectors $\vec{a}$ and $\vec{b}$ is $\vec{r} = \vec{a} + \lambda(\vec{b} - \vec{a})$.Substituting the values,we get $\vec{r} = -\hat{i} + 2\hat{k} + \lambda(4\hat{i} + 4\hat{j} + 4\hat{k})$.

Find the vector equation for the line passing through the points $(-1, 0, 2)$ and $(3, 4, 6).$

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