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Q.

Three lines L1  :  r=λi^,  λL2  :  r=k^+μj^,  μL3  :  r=i^+j^+νk^,  ν  are given. For which the points Q on L2  can we find P on L1and a point R on L3 so that P, Q,R are collinear

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a

k^+12j^

b

k^+j^

c

k^

d

k^12j^

answer is A, B.

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Detailed Solution

Position vector of point P  is p=λi^

Position vector of Q is q^=μj^+k^

Position vector of point R is r=i^+j^+rk^

PQR are collinear. Hence x(PQ)=y(PR)

x-λi+μj+k=y1-λi+j+rk It gives    xy=1λλ=1μ=r

q=1rj^+k^ or q=λλ-1j^+k^, where r0,λ0,λλ-11

μ0,1

 Hence, qk^ or j^+k^

 

 

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