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Question

If the non zero vectors a and b are perpendicular to each other then the solution of the equation r×a=b is

A
r=xa+1a.a(a×b)
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B
r=xb1b.b(a×b)
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C
r=x(a×b)
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D
none of these
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Solution

The correct option is A r=xa+1a.a(a×b)
Given: ab

[a.b=0]

Since, a.b=abcos90

Since, a,b,a×b are non-
coplanar;

r=xa+yb+z(a×b)......Eq:01

Solve b=r×a......(given);

b={xa+yb+z(a×b)}×a

b={0+y(b×a)+z((a×b)×a)}

b={y(b×a)z(a×(a×b))}


b={y(b×a)+z[(a.b)a(a.a)b]}

b={y(b×a)+z(a.a)b}

y=0,z=1a.a=1|a|2

Substitute the above values in Eq:01;
r=xa+1|a|2(a×b)

Option (A) is correct.






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