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AP EAMCET Engineering 2018 Apr 22 Shift 1 Paper
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Section:
Mathematics
© examsiri.com
Question :
33 of 160
Marks:
+1
,
-0
If
−
a
,
−
b
and
−
c
are mutually perpendicular vectors of the same magnitude, then the cosine of the angle between
−
a
and
−
a
+
−
b
+
−
c
is
1
√
2
1
√
3
1
2
√
3
2
Validate
Solution:
It is assumed.
Now.
|
a
+
b
+
c
|
2
=
(
a
+
b
+
c
)
.
(
a
+
b
+
c
)
|
a
|
2
+
|
b
|
2
+
|
c
|
2
=
2
(
a
.
b
+
b
.
c
+
c
.
a
)
|
a
|
2
+
|
b
|
2
+
|
c
|
2
=
λ
2
+
λ
2
+
λ
2
+
2
(
0
)
=
3
λ
2
|
a
+
b
+
c
|
=
√
3
λ
Let the angle between
a
and
a
+
b
+
c
is
θ
∴
cos
‌
θ
=
a
(
a
+
b
+
c
)
|
a
|
|
a
+
b
+
c
|
=
|
a
|
2
|
a
|
|
a
+
b
+
c
|
cos
‌
θ
=
λ
2
λ
+
√
3
λ
=
1
√
3
© examsiri.com
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