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Byju's Answer
Standard XII
Mathematics
Functions
If |a⃗+b⃗|=60...
Question
If
∣
∣
→
a
+
→
b
∣
∣
=
60
,
∣
∣
→
a
−
→
b
∣
∣
=
40
and
|
→
a
|
=
22
then find
∣
∣
→
b
∣
∣
.
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Solution
As
∣
∣
→
a
+
→
b
∣
∣
2
+
∣
∣
→
a
−
→
b
∣
∣
2
=
2
(
|
→
a
|
2
+
∣
∣
→
b
∣
∣
2
)
⇒
60
2
+
40
2
=
2
(
22
2
+
∣
∣
→
b
∣
∣
2
)
⇒
∣
∣
→
b
∣
∣
2
=
2116
Hence
∣
∣
→
b
∣
∣
=
46.
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13
Similar questions
Q.
If
|
→
a
+
→
b
|
=
60
,
|
→
a
−
→
b
|
=
40
,
and
|
→
b
|
=
46
. Find
|
→
a
|
Q.
If for vectors
→
a
and
→
b
,
|
→
a
|
=
4
,
∣
∣
→
b
∣
∣
=
3
and
→
a
→
b
=
8
, then find
∣
∣
→
a
×
→
b
∣
∣
.
Q.
I : If
|
→
a
+
→
b
|
=
|
→
a
−
→
b
|
, then
(
→
a
,
→
b
)
=
π
2
.
II : If
→
a
,
→
b
,
→
a
+
→
b
are unit vectors, then
(
→
a
,
→
b
)
=
2
π
3
.
Q.
If
→
a
and
→
b
are unequal vectors such that
(
→
a
−
→
b
)
×
[
(
→
b
+
→
a
)
×
(
2
→
a
+
→
b
)
]
=
→
a
+
→
b
, then the angle
θ
between
→
a
and
→
b
is
Q.
If
→
r
×
→
a
=
→
b
×
→
a
;
→
r
×
→
b
=
→
a
×
→
b
;
→
a
≠
0
,
→
b
≠
0
,
→
a
≠
λ
→
b
;
→
a
is not perpendicular to
→
b
, then
→
r
=
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