The plane $p$ passes through the points with coordinates $(4, -1, -3)$, $(-2, -5, 2)$ and \((4

Question

The plane $p$ passes through the points with coordinates $(4, -1, -3)$, $(-2, -5, 2)$ and $(4, -3, -2)$. Find a Cartesian equation of $p$. The line $l_1$ has equation $\frac{x-1}{2} = \frac{y-2}{-4} = \frac{z+3}{1}$ and the line $l_2$ has equation $\frac{x+2}{1} = \frac{y-1}{5} = \frac{z-3}{k}$, where $k$ is a constant. It is given that $l_1$ and $l_2$ intersect. Find the value of $k$. Show that $l_1$ lies in $p$ and find the coordinates of the point at which $l_2$ intersects $p$. Find the acute angle between $l_2$ and $p$.

Accepted Answer

$p: x + y + 2z = -3; \quad k = -7; \quad (-1, 6, -4); \quad \theta = 22.2^\circ$

N2011 P1 Q11

N2011 P1 Q11

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