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Byju's Answer
Standard XII
Mathematics
Parametric Equation of Normal
The reflectio...
Question
The reflection of the point with position vector
→
a
in the plane
→
r
.
→
n
=
q
is
A
→
a
+
(
→
q
−
→
a
.
→
n
)
|
→
n
|
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B
→
a
+
2
[
(
→
q
−
→
a
.
→
n
)
|
→
n
|
2
]
→
n
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C
→
a
+
2
(
→
q
+
→
a
.
→
n
)
|
→
n
|
→
n
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D
none of these
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Solution
The correct option is
A
→
a
+
2
[
(
→
q
−
→
a
.
→
n
)
|
→
n
|
2
]
→
n
→
P
R
=
→
r
−
→
a
and
→
P
Q
=
2
→
P
R
=
2
(
→
r
−
→
a
)
→
a
1
=
−
−
→
O
Q
=
−
−
→
O
P
+
−
−
→
P
Q
→
a
1
=
→
a
+
2
(
→
r
−
→
a
)
;
→
r
=
λ
→
n
+
→
a
so ,
(
λ
→
n
+
→
a
)
.
→
n
=
q
⇒
⇒
λ
=
→
q
−
→
a
.
→
n
(
→
n
)
2
so,
→
a
1
=
→
a
+
2
[
→
q
−
→
a
.
→
n
(
→
n
)
2
]
→
n
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Similar questions
Q.
Show that the angle between the line
→
r
=
→
a
+
λ
→
b
and plane
→
r
.
→
n
=
d
is
π
2
−
cos
−
1
(
→
b
.
→
n
|
→
b
|
|
→
n
|
)
.
Q.
If
→
n
is a unit vector in the direction of the vector
→
A
, then:
Q.
The angular momentum of a particle relative to a certain point
O
varies with time as
→
M
=
a
+
→
b
t
2
, where
→
a
and
→
b
are constant vectors, with
→
a
⊥
→
b
. If the force moment
→
N
relative to the point
O
acting on the particle when the angle between the vectors
→
N
and
→
M
equals
45
∘
is given as
→
N
=
x
√
a
b
→
b
. Find
x
.
Q.
If
→
ℓ
,
→
m
,
→
n
are three non-coplanar vectors and
→
a
,
→
b
are two vectors, then prove that
[
→
ℓ
,
→
m
,
^
n
]
(
→
a
,
→
b
)
=
∣
∣ ∣ ∣
∣
→
ℓ
.
→
a
→
ℓ
.
→
b
→
ℓ
→
m
.
→
a
→
m
.
→
b
→
m
→
n
.
→
a
→
n
.
→
b
→
n
∣
∣ ∣ ∣
∣
Q.
A vector
→
n
is inclined to
x
−
axis is at
45
o
to
y
−
axis at
60
o
an acute angel to
z
−
axis. If
→
n
is a normal to a plane passing through the points
(
√
2
,
−
1
,
1
)
, then the equation of the plane is
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