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FIND UNIT VECTORS PERPENDICULAR TO THE PLANE DETERMINED BY THE POINTS P(1,-1,2) , Q(2,0,-1) AND R(0,2,1).

FIND UNIT VECTORS PERPENDICULAR TO THE PLANE DETERMINED BY THE POINTS P(1,-1,2) , Q(2,0,-1) AND R(0,2,1).

Grade:Select Grade

3 Answers

Y RAJYALAKSHMI
45 Points
8 years ago
The two vectors in the given plane is PQ & PR
PQ = (2 – 1) i + (0 + 1) j + (-1 – 2)k = i + j – 3k
PR = (0 – 1)i + (2 + 1) j + (1 – 2k = –i + 3j – k
 
The vector perpendicular to PQ & PR is PQ x PR
= 8i + 4j + 4k
 
So, The unit vector perpendicular to the plane is (8i + 4j + 4k)/ sq. root ( 82 + 42+ 42)
= (2i + j + k )/sq. root (6)
 
 
 
 
Bharat Makkar
34 Points
8 years ago
THANKS!!!!
 
SHAIK HAFEEZUL KAREEM
109 Points
6 years ago
 
The two vectors in the given plane is PQ & PR
PQ = (2 – 1) i + (0 + 1) j + (-1 – 2)k = i + j – 3k
PR = (0 – 1)i + (2 + 1) j + (1 – 2k = –i + 3j – k
 
The vector perpendicular to PQ & PR is PQ x PR
= 8i + 4j + 4k
 
So, The unit vector perpendicular to the plane is (8i + 4j + 4k)/ sq. root ( 82 + 42+ 42)
= (2i + j + k )/sq. root (6)
 
 
 

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