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Let a=2i+j+k, b=i+2j-k and a unit vector c be co planar. If c is perpendicular to a, then c =

Let a=2i+j+k, b=i+2j-k and a unit vector c be co planar. If c is perpendicular to a, then c =

Grade:12th pass

1 Answers

sonika p
129 Points
5 years ago
let c = xi+yj+zk
given the two vectors are coplanar, thus their determinant is zero. 
equating the det to zero be get, -x+y+z=0
x=y+z.....(1)
and c is perpendicular to a, thus a.c=0
2x+y+z=0....(2)
from equation 1 and 2 we get, x=0
now, c is a unit vector, thus x2+y2+z2=1....(3)
and y+z=0...(4)
solving equations 3 and 4 we get y=+/- (1/root2)
thus z = -/+(1/root2)
thus c = (1/root2) j – (1/root2) k
or  c = – (1/root2) j + (1/root2) k
 

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