A line drawn from a point A(-2,-2,3) and para | vedclass

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(D) The equation of the line passing through $A(-2,-2,3)$ and parallel to the vector $\vec{v} = -2\hat{i} + 2\hat{j} - \hat{k}$ is given by: $\frac{x+

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$(0,-4,4)$

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(D) The equation of the line passing through $A(-2,-2,3)$ and parallel to the vector $\vec{v} = -2\hat{i} + 2\hat{j} - \hat{k}$ is given by: $\frac{x+2}{-2} = \frac{y+2}{2} = \frac{z-3}{-1} = \lambda$ Any point on this line can be represented as $(-2\lambda - 2, 2\lambda - 2, -\lambda + 3)$. Since the point $P$ lies on the $YOZ-$ plane,its $x-$coordinate must be $0$. Setting the $x-$coordinate to $0$: $-2\lambda - 2 = 0 \Rightarrow -2\lambda = 2 \Rightarrow \lambda = -1$. Substituting $\lambda = -1$ into the general coordinates: $x = -2(-1) - 2 = 0$ $y = 2(-1) - 2 = -4$ $z = -(-1) + 3 = 4$ Thus,the coordinates of point $P$ are $(0, -4, 4)$.

$A$ line drawn from a point $A(-2,-2,3)$ and parallel to the line $\frac{x}{-2}=\frac{y}{2}=\frac{z}{-1}$ meets the $YOZ-$ plane in point $P$. Then,the coordinates of the point $P$ are:

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