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Question

If ¯z1=a^i+b^j and ¯z2=c^i+d^j are two vectors in ^i and ^j system where |¯z1|=|¯z2|=r and ¯z1¯z2=0, then ¯ω1=a^i+c^j and ¯ω2=b^i+d^j satisfy

A
|¯ω1|=r
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B
|¯ω2|r
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C
¯ω1,¯ω2=0
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D
None of these
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Solution

The correct option is A |¯ω1|=r
The first condition gives a2+b2=r2 and c2+d2=r2
z1z2=0 gives ac+bd=0
Substituting b=acd in the above equation, we get
a2+a2c2d2=r2
a2(c2+d2d2)=r2
a=d
w1=a2+c2=c2+d2=r

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