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Question

Let r=a+λl and r=b+μm be two lines in space where a=5^i+^j+2^k. b=^i+7^j+8^k, l=4^i+^j^k]and m=2^i5^j7^(k then the p.v. of a point which lies on both of these lines, is

A
^i+2^j+^k
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B
2^i+^j+^k
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C
^i+^j+2^k
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D
non existent as the lines are skew
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Solution

The correct option is D non existent as the lines are skew
1st line ¯r=¯a+λ¯l
x54=y11=z21=RR is constant
2nd line ¯r=¯b+μ¯m
x+12=y75=z87=μμ is constant
x=4R+5y=R+1z=R+2
x=2μ1y=5μ+7z=7μ+8
4R+5=2μ1....(1)
R+1=5μ+7....(2)
R+2=7μ+8....(3)
From (1) & (2)
4R2μ=6+R+5μ=65R+3μ=0R=3μ5
Substituting R=3μ5 in (3)
LHS=R+2=(3μ5)+2=3μ5+2
RHS=7μ+8 LHSRHS
Lines do not intresed
They are skew lines.

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