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Find the unit vector coplanar with i+j+2k and i+2j+k and perpendicular to i+j+k.?

Find the unit vector coplanar with i+j+2k and i+2j+k and perpendicular to i+j+k.?

Question Image
Grade:12th pass

1 Answers

Arun
25763 Points
3 years ago
Let the required vector is xa + yb
 r = x(i + j +2k) + y (i + 2j + k)
 = (X+y)i + (x+2y)j + (2x + y)k
 
Now it should be perpendicular to i + j + k
 
Hence
r . (i+j+k) = 0
 
x+y + 2x + y + x +2y = 0
 
x+ y = 0
 
Now
r should be a unit vector hence
sqrt((x+y)² +(x+2y)² + (2x+y)²) = 1
 
Solve both the equations
 
r will come out as
 
r = +- (j+k)/sqrt(2)
 

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