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Question

If x×y=a, y×z=b, xb=γ, xy=1 and yz=1. Vector z is

A
γ|a×b|2[a+b×(a×b)]
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B
γ|a×b|2[a×ba×(a×b)]
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C
γ|a×b|2[a×b+b×(a×b)]
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D
None of these
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Solution

The correct option is C γ|a×b|2[a×b+b×(a×b)]
x×y=a (i)
y×z=b (ii)
xb=γ (iii)
xy=1 (iv)
yz=1 (v)

From (ii), x(y×z)=xb=γ
[xyz]=γ

From (i) and (ii),
(x×y)×(y×z)=a×b
[xyz]y[yyz]x=a×b
or y=a×bγ (vi)

Also from (ii),
(y×z)×y=b×y
|y|2z(zy)y=b×y
z=1|y|2[y+b×y]
=γ|a×b|2[a×b+b×(a×b)]

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