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Question

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

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Solution

b=xi+yi+zk
Now,
ab=x+y+x=3
aαb=(i+j+k)α(xi+yi+zk)
=((zy)i+(xz)i+(yx)k)=jk
Now,
zy=0
z=y
x2=1 and yx=1
x+y+z=3
1+2+2+2=3
z=2/3
y=2/3
x=5/3
b=(5i+2j+2k)/3

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