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Question

If A=2i+k,B=i+j+k and C=4i3j+7k, then a vector r which satisfies R×B=C×B and R.A=0, is

A
i8j+2k
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B
i8j+2k
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C
i+8j+2k
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D
none of these
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Solution

The correct option is A i8j+2k
Let R=xi+yj+zk
R.A=02x+z=0 ....(1)
R×B=C×B∣ ∣ijkxyz111∣ ∣=∣ ∣ijk437111∣ ∣(yz)i+(zx)j+(xy)k=10i+3j+7k
yz=10 ...(2)
zx=3 ...(3)
and xy=7
Solving (1) and (2), we get x=1,z=2
From (2), y=8
Hence R=i8j+2k

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