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BITSAT 2017 Slot 2 Solved Paper
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© examsnet.com
Question : 140
Total: 150
Let
^
a
and
^
b
be two non-collinear unit vectors. If
u
=
^
a
−
(
^
a
.
^
b
)
^
b
and
v
=
^
a
×
^
b
, then
|
v
|
is equal to
|
u
|
|
u
|
+
|
v
.
^
a
|
2
v
|
|
v
|
+
u
.
(
^
a
+
^
b
)
Validate
Solution:
v
=
^
a
×
^
b
=
|
a
|
|
b
|
sin
θ
^
n
=
sin
θ
^
n
Where,
θ
is the angle between
a
and
b
.
[
∵
|
a
|
=
1
=
|
b
|
]
∴
[
V
]
=
sin
θ
Now,
u
=
^
a
−
(
^
a
.
^
b
)
^
b
=
^
a
−
(
cos
θ
)
^
b
⇒
|
u
|
2
=
(
^
a
−
(
cos
θ
)
^
b
)
.
(
^
a
−
cos
θ
)
^
b
)
=
a
2
+
cos
2
θ
b
2
−
2
cos
θ
a
b
[
|
a
|
2
=
|
b
|
2
=
|
a
|
|
b
|
=
1
]
=
1
+
cos
2
θ
−
2
cos
2
θ
=
1
−
cos
2
θ
=
sin
2
θ
∴
|
u
|
=
sin
θ
Thus
|
v
|
=
|
u
|
© examsnet.com
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