If →a=^i−2^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
^i−3^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 ⇒(λ−1)¯¯¯a=(μ−1)¯¯b ⇒λ=1,μ=1 as ¯¯¯aׯ¯b are non collinear. Hence point of intersection ¯¯¯r=¯¯¯a+¯¯b=(i−j+2k)