Question

The |⃗A +B ⃗⃗| = |⃗A| + |⃗⃗B|, then angle

between ⃗A ⃗⃗B will be​

Answer 1

Answer:

⃗+⃗=−⃗
a
→
+
b
→
=
−
c
→

Taking self dot product we get

(⃗+⃗)⋅(⃗+⃗)=(−⃗)⋅(−⃗)
(
a
→
+
b
→
)
⋅
(
a
→
+
b
→
)
=
(
−
c
→
)
⋅
(
−
c
→
)

2+⃗⋅⃗+⃗⋅⃗+2=2
a
2
+
a
→
⋅
b
→
+
a
→
⋅
b
→
+
b
2
=
c
2

2⃗⋅⃗=2−2−2
2
a
→
⋅
b
→
=
c
2
−
a
2
−
b
2

2cos=2−2−2
2
a
b
cos
⁡
θ
=
c
2
−
a
2
−
b
2

cos=2−2−22
cos
⁡
θ
=
c
2
−
a
2
−
b
2
2
a
b

Now, setting the values of =3,=5,=7
a
=
3
,
b
=
5
,
c
=
7
, the angle (
θ
) between ⃗
a
→
& ⃗
b
→
is given as

cos=72−32−522⋅3⋅5
cos
⁡
θ
=
7
2
−
3
2
−
5
2
2
⋅
3
⋅
5

cos=12
cos
⁡
θ
=
1
2

cos=cos60∘
cos
⁡
θ
=
cos
⁡
60
∘

=60∘
θ
=
60
∘



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