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Question

A,B,C are three vectors given by 2i+k,i+j+k and 4i3j+7k. Then, find R which satisfies the relation R×B=C×B and RA=0.

A
R=i16j2k
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B
R=i8j+2k
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C
R=2i+8j+2k
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D
R=i+8j+4k
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Solution

The correct option is C R=i8j+2k
Given A=2i+k , B=i+j+k and C=4i3j+7k
Let R be xi+yj+zk
Given R.A=0
2x+z=0
Given (RC)×B=0
((x4)i+(y+3)j+(z7)k)×(i+j+k)=0
(yz+10)i(xz+3)j+(xy7)k=0
zy=10,zx=3,xy=7
By solving above three equations , we get x=1,y=8,z=2
Therefore R=i8j+2k

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