The parametric equations of the line passing | vedclass

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(C) The vector equation of a line passing through points $A(\vec{a})$ and $B(\vec{b})$ is given by $\vec{r} = \vec{a} + \lambda(\vec{b} - \vec{a})$.He

Vedclass · Accepted Answer

$x=3-2 \lambda, \quad y=4-5 \lambda, \quad z=-7+13 \lambda$

Vedclass · Answer

(C) The vector equation of a line passing through points $A(\vec{a})$ and $B(\vec{b})$ is given by $\vec{r} = \vec{a} + \lambda(\vec{b} - \vec{a})$.Here,$\vec{a} = 3\hat{i} + 4\hat{j} - 7\hat{k}$ and $\vec{b} = \hat{i} - \hat{j} + 6\hat{k}$.The direction vector $\vec{v} = \vec{b} - \vec{a} = (1-3)\hat{i} + (-1-4)\hat{j} + (6 - (-7))\hat{k} = -2\hat{i} - 5\hat{j} + 13\hat{k}$.Thus,the parametric equations are $x = x_1 + v_x \lambda$,$y = y_1 + v_y \lambda$,$z = z_1 + v_z \lambda$.Substituting the values: $x = 3 - 2\lambda$,$y = 4 - 5\lambda$,$z = -7 + 13\lambda$.

The parametric equations of the line passing through the points $A(3,4,-7)$ and $B(1,-1,6)$ are

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