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Chapter 12: Q. 30 (page 976)

In Exercises 27鈥�30, use the result from Example 4 to find the distance from the point P to the given plane.P=(鈭�3,2,6),x=3y+5z

Short Answer

Expert verified

Thedistancefromthegivenpointtothegivenplaneis:D=3935.

Step by step solution

01

Step 1. Given information  

Apoint,P=(鈭�3,2,6);aplane,x-3y-5z=0

02

Step 2. Finding the distance from the given point to the given plane

ThedistancefromthepointP(x0,y0,z0)totheplanewithequationax+by+cz=disgivenby,D=|ax0+by0+cz0鈭�d|a2+b2+c2.Substitutingthegivenvalues,weget,D=|1脳-3+-3脳2+-5脳6-0|12+-32+-52鈬�D=|-3-6-30-0|1+9+25鈬�D=|-39|35鈬�D=3935

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