2.
If a and b are unit vectors such that a xb is also a unit vector, then
the angle between a and b
Answers
Answer:
also unit vector
To find: Angle B/w
a
and
b
Suppose angle b/w
a
and
b
is θ
a
.
b
=∣
a
∣∣
b
∣cosθ (Dot product of two vectors)
a
.
b
=cosθ as
a
and
b
are unit vector so ∣
a
∣=∣
b
∣=1
3
a
−
b
is also unit vector i.e. ∣
3
a
−
b
∣=1
(
3
a
−
b
)
2
=1⇒(
3
)
2
∣
a
∣
2
+∣
b
∣
2
−2
3
∣
a
.
b
∣=1
3(1)+(1)−2
3
cosθ=1 as
a
.
b
=cosθ
So, 4−2
3
cosθ=1⇒3=2
3
cosθ
cosθ=
2
3
i.e θ=
6
2
or 30
o
Answer:
30 degrees
Step-by-step explanation:
and
b
are unit vectors and (
3
a
−
b
) is also unit vector
To find: Angle B/w
a
and
b
Suppose angle b/w
a
and
b
is θ
a
.
b
=∣
a
∣∣
b
∣cosθ (Dot product of two vectors)
a
.
b
=cosθ as
a
and
b
are unit vector so ∣
a
∣=∣
b
∣=1
3
a
−
b
is also unit vector i.e. ∣
3
a
−
b
∣=1
(
3
a
−
b
)
2
=1⇒(
3
)
2
∣
a
∣
2
+∣
b
∣
2
−2
3
∣
a
.
b
∣=1
3(1)+(1)−2
3
cosθ=1 as
a
.
b
=cosθ
So, 4−2
3
cosθ=1⇒3=2
3
cosθ
cosθ=
2
3
i.e θ=
6
2
or 30
o