Tip:A–D to answerE for explanationV for videoS to reveal answer
If the lines 2x−1=−32−y=αz−3 and 5x−4=2y−1=βz intersect, then the magnitude of the minimum value of 8αβ is
- A.
18
(Correct Answer) - B.
17
- C.
16
- D.
15
Explanation
2x−1=−32−y=αz−3
5x−4=2y−1=βz
Coplanar condition
=25−3amp;3amp;2amp;1amp;αamp;βamp;3=0
⇒α−β=3⇒α=β+3
Given expression
=8(β2+3β+49−49)=8(β+23)2−18
So magnitude of minimum value =18
Explanation
2x−1=−32−y=αz−3
5x−4=2y−1=βz
Coplanar condition
=25−3amp;3amp;2amp;1amp;αamp;βamp;3=0
⇒α−β=3⇒α=β+3
Given expression
=8(β2+3β+49−49)=8(β+23)2−18
So magnitude of minimum value =18
