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Test Index
JEE Main 27-Jan-2024 Shift 2 Solved Paper
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Section:
Mathematics
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© examsnet.com
Question : 20
Total: 90
Let the position vectors of the vertices
A
,
B
and
C
of a triangle be
2
^
i
+
2
^
j
+
^
k
,
^
i
+
2
^
j
+
2
^
k
and
2
^
i
+
^
j
+
2
^
k
respectively. Let
l
1
,
l
2
and
l
3
be the lengths of perpendiculars drawn from the ortho center of the triangle on the sides
AB
,
BC
and
CA
respectively, then
l
1
2
+
l
2
2
+
l
3
2
equals :
[27-Jan-2024 Shift 2]
1
5
1
2
1
4
1
3
Validate
Solution:
👈: Video Solution
△
ABC
is equilateral
Orthocentre and centroid will be same
G
(
5
3
,
5
3
,
5
3
)
Mid-point of
AB
is
D
(
3
2
,
2
,
3
2
)
∴
ℓ
1
=
√
1
36
+
1
9
+
1
36
ℓ
1
=
√
1
6
=
ℓ
2
=
ℓ
3
∴
ℓ
1
2
+
ℓ
2
2
+
ℓ
3
2
=
1
2
© examsnet.com
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