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Question

The equation of the line passing through (4,3,1), parallel to the plane x+2yz5=0 and intersecting the line x+13=y32=z21 is:

A
x+41=y31=z11
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B
x+41=y31=z13
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C
x+43=y31=z11
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D
x+42=y31=z14
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Solution

The correct option is C x+43=y31=z11
Vector passing through (4,3,1) and (1,3,2)=3^i+^k
Normal vector of plane containing two intersecting lines is parallel to the vector.
r1=∣ ∣ ∣^i^j^k301321∣ ∣ ∣=2^i+6^k

Required line is parallel to the vector.
r2=∣ ∣ ∣^i^j^k121206∣ ∣ ∣=3^i^j+^k
Required equation of line passing through (4,3,1) is x+43=y31=z11

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