A) \[7x\text{ }+\text{ }2y\text{ }+\text{ }4z\text{ }=\text{ }54~~\]
B) \[3x\text{ }+\text{ }4y\text{ }+\text{ }5z\text{ }=\text{ }49\]
C) \[4x\text{ }+\text{ }3y\text{ }+\text{ }5z\text{ }=\text{ }50\]
D) \[5x\text{ }+\text{ }4y\text{ }+\text{ }3z\text{ }=\text{ }57\]
Correct Answer: C
Solution :
Given equation of lines are \[\frac{x-1}{3}=\frac{y-2}{1}=\frac{z-3}{2}\] ?(1) and\[\frac{x-3}{1}=\frac{y-1}{2}=\frac{z-2}{3}\] ?(2) Any point on line (1) is \[P(3\lambda +1,\lambda +2,2\lambda +3)\]and on line (2) is\[Q(\mu +3,2\mu +1,3\mu +2).\]On solving \[3\lambda +1=\mu +3\] and\[\lambda +2=2\mu +1\]we get \[\lambda =1,\mu =1\] \[\therefore \]Point of intersection of two lines is R (4, 3, 5) So, equation of plane ^ to OR where O is (0, 0, 0) and passing through R is\[4x+3y+5z=50\]
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