Q27 of 181 Page 1181

Show that the line is parallel to the plane

Given :


Equation of plane : :


Equation of a line :



To Prove : Given line is parallel to the given plane.


Comparing given plane i.e.



with , we get,



This is the vector perpendicular to the given plane.


Now, comparing the given the equation of line i.e.



with , we get,



Now,




= 1 – 5 + 4


= 0



Therefore, a vector normal to the plane is perpendicular to the vector parallel to the line.


Hence, the given line is parallel to the given plane.


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25

Find the distance of the point A(-1, -5, -10) from the point of intersection of the line and the plane

HINT: Convert the equations of the line and the plane to Cartesian form.


 26

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 28

Find the equation of a plane which is at a distance of 3√3 units from the origin and the normal to which is equally inclined to the coordinate axes.

 29

A vector of magnitude 8 units is inclined to the x-axis at 45o, y-axis at 60o and an acute angle with the z-axis, if a plane passes through a point (√2, -1, 1) and is normal to find its equation in vector form.