Practicing Success
The equation of the plane containing two lines $\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-0}{3}$ and $ \frac{x}{-2}=\frac{y-2}{-3}=\frac{z+1}{-1}$, is |
$8x + y - 5z - 7 = 0 $ $8x + y + 5z - 7 = 0 $ $8x - y - 5z - 7 = 0 $ none of these |
none of these |
Lines: $\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-0}{3}$ and $ \frac{x}{-2}=\frac{y-2}{-3}=\frac{z+1}{-1}$ vectors parallel to given lines $\vec{b_1}=2\hat i-\hat j+3\hat k$, $\vec{b_2}=-2\hat i-3\hat j-\hat k$ $\vec n$ (normal to plane) = $\vec{b_1}×\vec{b_2}$ $=\begin{vmatrix}\hat i&\hat j&\hat k\\2&-1&3\\-2&-3&-1\end{vmatrix}=10\hat i-4\hat j-8\hat k$ lines pass through points (1, -1, 0) and (0, 2, -1) considering (1, -1, 0) we get equation of plane $10×(x-1)-4×(y+1)-8(z)=0$ $10x-10-4y-4-8z=0$ so $10x-4y-8z=14$ $5x-2y-4z=7$ |