If magnitudes of dot and cross products of two vectors are equal then the angle between them is:
1)45°
2)60°
3)90°
Answers
Answered by
2
Answer:
Correct option is C)
Step 1: Simplify the given equation
Let the two vectors be
A
and
B
Magnitude of Cross product of vectors=
3
× Magnitude of Dot product of vectors
⇒∣
A
×
B
∣=
3
∣
A
.
B
∣
Squaring on both the sides
∣
A
×
B
∣
2
=3∣
A
.
B
∣
2
⇒ (
A
×
B
)(
A
×
B
)=3(
A
.
B
)(
A
.
B
)
⇒ (∣
A
∣∣
B
∣sinθ)(∣
A
∣∣
B
∣sinθ)=(∣
A
∣∣
B
∣cosθ)(∣
A
∣
B
∣cosθ) ....(1)
Step 2: Angle between the Vectors
Eq (1) ⇒ sin
2
θ=3cos
2
θ
⇒ tan
2
θ=3
⇒ θ=tan
−1
(
3
)=
3
π
Hence, Option C is correct.
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