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Question: Answered & Verified by Expert
If the straight linc $\frac{x-x_{0}}{\ell}=\frac{y-y_{0}}{m}=\frac{z-z_{0}}{n}$ is parallcl to the plane $a x+b y+c z+d=0$ then which one of the following is correct?
MathematicsThree Dimensional GeometryNDANDA 2013 (Phase 1)
Options:
  • A $\ell+\mathrm{m}+\mathrm{n}=0$
  • B $a+b+c=0$
  • C $\frac{\mathrm{a}}{\ell}+\frac{\mathrm{b}}{\mathrm{m}}+\frac{\mathrm{c}}{\mathrm{n}}=0$
  • D $\mathrm{a} \ell+\mathrm{bm}+\mathrm{cn}=0$
Solution:
1033 Upvotes Verified Answer
The correct answer is: $\mathrm{a} \ell+\mathrm{bm}+\mathrm{cn}=0$
If the line is parallel to the plane then $\mathrm{a} \ell+\mathrm{bm}+\mathrm{cn}=0$

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