5.
If two vectors are Ā= i + i + and B=-1 -j-k, then find the angle between (A-B ) and Ā.
Answers
Answer:
Explanation:
Let the angle between two vectors
A
and
B
be
θ
So
|
A
+
B
|
2
=
|
A
|
2
+
|
B
|
2
+
2
|
A
|
|
B
|
cos
θ
Again
|
A
−
B
|
2
=
|
A
|
2
+
|
B
|
2
+
2
|
A
|
|
B
|
cos
(
180
−
θ
)
By the given condition
|
A
+
B
|
=
|
A
−
B
|
So
cos
θ
=
cos
(
180
−
θ
)
⇒
θ
=
180
−
θ
⇒
θ
=
90
∘Let the angle between two vectors
A
and
B
be
θ
So
|
A
+
B
|
2
=
|
A
|
2
+
|
B
|
2
+
2
|
A
|
|
B
|
cos
θ
Again
|
A
−
B
|
2
=
|
A
|
2
+
|
B
|
2
+
2
|
A
|
|
B
|
cos
(
180
−
θ
)
By the given condition
|
A
+
B
|
=
|
A
−
B
|
So
cos
θ
=
cos
(
180
−
θ
)
⇒
θ
=
180
−
θ
⇒
θ
=
90
∘Let the angle between two vectors
A
and
B
be
θ
So
|
A
+
B
|
2
=
|
A
|
2
+
|
B
|
2
+
2
|
A
|
|
B
|
cos
θ
Again
|
A
−
B
|
2
=
|
A
|
2
+
|
B
|
2
+
2
|
A
|
|
B
|
cos
(
180
−
θ
)
By the given condition
|
A
+
B
|
=
|
A
−
B
|
So
cos
θ
=
cos
(
180
−
θ
)
⇒
θ
=
180
−
θ
⇒
θ
=
90
∘