Q1 of 230 Page 29

Find the distance of the point from the plane

Given:


* Point given by the equation:


* Plane given by the equation: , where the normal vector is:


We know, the distance of from the plane is given by:



Putting the values of and :


⟹


⟹ units


the distance of the point from the plane


is units


More from this chapter

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18

Find the equation of the plane which contains the line of intersection of the plane x + 2y + 3z – 4 = 0 and 2x + y – z + 5 = 0 and whose x – intercept is twice of z – intercept. Hence, write the equation of the plane passing through the point (2,3, – 1) and parallel to the plane obtained above?

 19

Find the equation of the plane through the line of intersection of the plane x + y + z = 1 and 2x + 3y + 4z = 5 and twice of its y–intercept is equals to the three times its z intercept?

 2

Show that the points and are equidistant from the plane

3

Find the distance of the point (2, 3, –5) from the plane x + 2y – 2z – 9 = 0.