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Question

If a=^i2^j+^k,b=^j+^k, then the point of intersection of lines r×a=b×a and r×b=a×b is

A
^i+^j+^k
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B
^i3^j
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C
^i^j+2^k
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D
3^i^j+^k
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Solution

The correct option is C ^i^j+2^k
Line 1, ¯¯¯rׯ¯¯a=¯¯bׯ¯¯a
(¯¯¯r¯¯b)ׯ¯¯a=0
¯¯¯r¯¯b=λ¯¯¯a
¯¯¯r=b+λ¯¯¯a
Line 2, ¯¯¯rׯ¯b=¯¯¯aׯ¯b
(¯¯¯r¯¯¯a)ׯ¯b=0
¯¯¯r=¯¯¯a+μ¯¯b
for point of intersection
b+λ¯¯¯a=a+μ¯¯b
(λ1)¯¯¯a=(μ1)¯¯b
λ=1,μ=1 as ¯¯¯aׯ¯b are non collinear.
Hence point of intersection ¯¯¯r=¯¯¯a+¯¯b=(ij+2k)

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