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Question

If a=^i+^j+^k,b=^j^k, then find a vector c such that a×c=banda.c=3.

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Solution


Let c=xˆi+yˆj+zˆk
a.c=3
(ˆi+ˆj+ˆk).(xˆi+yˆj+zˆk)=3
x+y+z=3
Also, a×c=b

∣ ∣ ∣ˆiˆjˆkxyz111∣ ∣ ∣=ˆjˆk

ˆi(yz)ˆj(xz)+ˆk(xy)=ˆjˆk
On comparing,
yz=0y=z
zx=1
xy=1
Solving the formed equations, we get,
x=13,y=43,z=43
Hence,
c=13ˆi+43ˆj+43ˆk


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