Q16 of 230 Page 30

Show that the plane whose vector equation is and the line whose vector equation is are parallel. Also, find the distance between them.

We know that line and plane is parallel if

……(1)


Given, equation of line
 and equation of plane is


,


So, and


Now,


=


= 2 + 2 – 4 = 0


So, the line and the plane are parallel


We know that the distance (D) of a plane from a point is given by







We take the mod value


So,


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Find the equation of the plane passing through the intersection of the planes x – 2y + z = 1 and 2x + y + z = 8 and parallel to the line with direction ratios proportional to 1, 2, 1. Find also the perpendicular distance of (1, 1, 1) from this plane.

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State when the line is parallel to the plane Show that the line is parallel to the plane Also, find the distance between the line and the plane.

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Find the equation of the plane through the intersection of the planes 3x – 4y + 5z = 10 and 2x + 2y – 3z = 4 and parallel to the line x = 2y = 3z.

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Find the vector and Cartesian forms of the equation of the plane passing through the point (1, 2, – 4) and parallel to the lines and Also, find the distance of the point (9, – 8, – 10) from the plane thus obtained.