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Standard XII
Mathematics
Distance Formula
Question
Let the distance between vectors are given as follows :
(
i
)
4
i
+
3
j
−
6
k
,
−
2
i
+
j
−
k
be
√
k
(
i
i
)
−
2
i
+
3
j
+
5
k
,
7
i
−
k
be
m
√
n
Find
k
−
(
m
∗
n
)
?
20
21
22
23
A
21
B
20
C
22
D
23
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Solution
Verified by Toppr
(i) Distance between
4
i
+
3
j
−
6
k
and
−
2
i
+
j
−
k
is given by
√
(
4
+
2
)
2
+
(
3
−
1
)
2
+
(
−
6
+
1
)
2
=
√
36
+
4
+
25
=
√
65
⇒
k
=
65
(ii) Distance between
−
2
i
+
3
j
+
5
k
and
7
i
−
k
would be
√
(
−
2
−
7
)
2
+
(
3
)
2
+
(
5
+
1
)
2
=
√
81
+
9
+
36
=
√
126
=
3
√
14
⇒
m
=
3
,
n
=
14
∴
k
−
(
m
∗
n
)
=
65
−
(
3
×
14
)
=
65
−
42
=
23
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Similar Questions
Q1
Let the distance between vectors are given as follows :
(
i
)
4
i
+
3
j
−
6
k
,
−
2
i
+
j
−
k
be
√
k
(
i
i
)
−
2
i
+
3
j
+
5
k
,
7
i
−
k
be
m
√
n
Find
k
−
(
m
∗
n
)
?
View Solution
Q2
Prove that the following vectors are coplanar:
(i)
2
i
^
-
j
^
+
k
^
,
i
^
-
3
j
^
-
5
k
^
and
3
i
^
-
4
j
^
-
4
k
^
(ii)
i
^
+
j
^
+
k
^
,
2
i
^
+
3
j
^
-
k
^
and
-
i
^
-
2
j
^
+
2
k
^
View Solution
Q3
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
Q4
Given two vectors
a
=
2
i
−
3
j
+
6
k
on
b
=
2
i
+
3
j
−
k
and
λ
=
t
h
e
p
r
o
j
e
c
t
i
o
n
o
f
a
o
n
b
t
h
e
p
r
o
j
e
c
t
i
o
n
o
f
b
o
n
a
,
then the value of
λ
is
View Solution
Q5
The points whose position vectors are
5
ˆ
i
+
5
ˆ
k
,
2
ˆ
i
+
ˆ
j
+
3
ˆ
k
and
−
4
ˆ
i
+
3
ˆ
j
−
ˆ
k
are collinear.
View Solution