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Standard XII
Mathematics
Section Formula
Question
The perimeter of the triangle whose vertices are the points
2
¯
i
−
¯
j
+
¯
k
,
¯
i
−
3
¯
j
−
5
¯
K
,
3
¯
i
−
4
¯
j
−
4
¯
j
−
4
¯
k
is
√
3
+
√
35
+
√
7
√
6
+
√
35
+
√
7
√
6
+
√
30
+
√
41
√
6
+
√
35
+
√
41
A
√
6
+
√
35
+
√
7
B
√
6
+
√
35
+
√
41
C
√
3
+
√
35
+
√
7
D
√
6
+
√
30
+
√
41
Open in App
Solution
Verified by Toppr
Given position vector
A
=
2
i
−
j
+
k
B
=
i
−
3
j
+
k
C
=
3
i
−
4
j
−
4
k
Perimeter
=
|
¯
¯¯¯¯¯¯
¯
A
B
|
+
|
¯
¯¯¯¯¯¯
¯
B
C
|
+
|
¯
¯¯¯¯¯¯
¯
C
A
|
|
¯
¯¯¯¯¯¯
¯
A
B
|
=
√
(
2
−
1
)
2
+
(
−
1
+
3
)
2
+
(
1
+
5
)
2
=
√
1
+
4
+
36
=
√
41
|
¯
¯¯¯¯¯¯
¯
B
C
|
=
√
(
3
−
1
)
2
+
(
−
4
+
3
)
2
+
(
−
4
+
5
)
2
=
√
4
+
1
+
1
=
√
6
|
¯
¯¯¯¯¯¯
¯
C
A
|
=
√
(
3
−
2
)
2
+
(
−
4
+
1
)
2
+
(
−
4
−
1
)
2
=
√
1
+
9
+
25
=
√
35
∴
Perimeter
=
√
6
+
√
35
+
√
41
.
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16
Similar Questions
Q1
The perimeter of the triangle whose vertices are the points
2
¯
i
−
¯
j
+
¯
k
,
¯
i
−
3
¯
j
−
5
¯
K
,
3
¯
i
−
4
¯
j
−
4
¯
j
−
4
¯
k
is
View Solution
Q2
The vectors
2
¯
i
−
3
¯
j
+
¯
k
,
¯
i
−
2
¯
j
+
3
¯
k
,
3
¯
i
+
¯
j
−
2
¯
k
View Solution
Q3
If
¯
r
=
3
¯
i
+
2
¯
j
−
5
¯
k
,
¯
a
=
2
¯
i
−
¯
j
+
¯
k
,
¯
b
=
¯
i
+
3
¯
j
−
2
¯
k
and
¯
c
=
−
2
¯
i
+
¯
j
−
3
¯
k
such that
¯
r
=
λ
¯
a
+
μ
¯
b
+
δ
¯
c
then
μ
,
λ
2
,
δ
are in
View Solution
Q4
If
¯
A
B
=
−
¯
i
−
2
¯
j
−
6
¯
k
,
¯
B
C
=
2
¯
i
−
¯
j
+
¯
k
,
¯
A
C
=
¯
i
−
3
¯
j
−
5
¯
k
. Then
∠
B
=
?
View Solution
Q5
If
¯
r
×
¯
b
=
¯
c
×
¯
b
,
¯
r
⋅
¯
a
=
0
,
¯
a
=
2
¯
i
+
3
¯
j
−
¯
k
,
¯
b
=
3
¯
i
−
¯
j
+
¯
k
,
¯
c
=
¯
i
+
¯
j
+
3
¯
k
then
¯
r
=
View Solution