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If L1, L2 and L3 are lines in a plane, is L1 perpendicular

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If L1, L2 and L3 are lines in a plane, is L1 perpendicular  [#permalink]

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New post 09 Apr 2011, 01:48
3
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

87% (00:49) correct 13% (01:00) wrong based on 149 sessions

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If L1, L2 and L3 are lines in a plane, is L1 perpendicular to L3?

1. L1 is perpendicular to L2
2. L2 is perpendicular to L3

This may seem like an easy one! But I haven't been able to crack it!!
Spoiler: OA

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Re: Perpendicular or not?  [#permalink]

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New post 09 Apr 2011, 02:17
petrifiedbutstanding wrote:
If L1, L2 and L3 are lines in a plane, is L1 perpendicular to L3?

1. L1 is perpendicular to L2
2. L2 is perpendicular to L3

This may seem like an easy one! But I haven't been able to crack it!!


Combining both, we can conclude that either \(L1 || L3\) OR "L1 coincides with L3"

\(L1 \hspace{3} \perp \hspace{3} L2\)

\(L2 \hspace{3} \perp \hspace{3} L3\)

\(L1 \hspace{3} || \hspace{3} L3\) OR "L1 coincides with L3" but "L1 is not perpendicular to L3"

Ans: "C"


1. L1 is perpendicular to L2

Attachment:
l1_perp_l2.PNG
l1_perp_l2.PNG [ 6.21 KiB | Viewed 9710 times ]


2. L2 is perpendicular to L3

Attachment:
l2_perp_l3.PNG
l2_perp_l3.PNG [ 6.94 KiB | Viewed 9707 times ]


Combining both:

Attachment:
l1_perp_l2_perp_l3.PNG
l1_perp_l2_perp_l3.PNG [ 4.28 KiB | Viewed 9693 times ]

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Re: Perpendicular or not?  [#permalink]

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New post 09 Apr 2011, 03:42
Hi Fluke,

Thanks. But doesn't the question clearly ask whether L1 is perp to L3, which is unanswerable with the given data?
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Re: Perpendicular or not?  [#permalink]

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New post 09 Apr 2011, 03:49
petrifiedbutstanding wrote:
Hi Fluke,

Thanks. But doesn't the question clearly ask whether L1 is perp to L3, which is unanswerable with the given data?


I don't think so. It is a Yes/No question.

The definitive answer to the question is: "No, L1 is NOT perpendicular to L3". Why do you think it's unanswerable, please explain.
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Re: Perpendicular or not?  [#permalink]

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New post 09 Apr 2011, 04:59
No, you're right. I wrongly analysed it with the second statement.
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Re: Perpendicular or not?  [#permalink]

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New post 14 Apr 2012, 12:21
petrifiedbutstanding wrote:
No, you're right. I wrongly analysed it with the second statement.

If lines are perpendicular then
m1.m2=-1

Acc to 1) L1 is perpendi to L2 => m1.m2=-1 => m2=-1/m1, also cnt deduce whether L1 is perpendi to L3

Acc to 2) L2 is perpendi to L3 =>. m2.m3=-1 => cnt deduce whether L1 is perpendi to L3

Combine 1) and 2)

-1/m1 * m3=-1 =>m3/m1=1

Definitely L1 not perpendi to L3

So C)
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Re: If L1, L2 and L3 are lines in a plane, is L1 perpendicular  [#permalink]

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New post 14 Apr 2012, 22:03
petrifiedbutstanding wrote:
If L1, L2 and L3 are lines in a plane, is L1 perpendicular to L3?

1. L1 is perpendicular to L2
2. L2 is perpendicular to L3

This may seem like an easy one! But I haven't been able to crack it!!


Explanation :

Just pictorial representation helps resolve the above equation

1: L1 P L2 ...
no mention of L3...hence NOT SUFFICIENT
hence A and D options are not the answers

2: L2 P L3
no mention of L1, hence NOT SUFFICIENT
Hence Option B Is not answer

so left with C & E

together L1 P L2 P L3
by this , we can see that L1 is parallel to L3...
hence L1 is not perpendicular to L3...hence C is the answer
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Re: If L1, L2 and L3 are lines in a plane, is L1 perpendicular  [#permalink]

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New post 23 Dec 2018, 08:44

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Re: If L1, L2 and L3 are lines in a plane, is L1 perpendicular   [#permalink] 23 Dec 2018, 08:44
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