Question

if the vector product and dot product are equal to each other then find the angle between the vector​

Answer 1

Answer :

The vector product and dot product of two vectors are equal to each other.

We have to find angle between the vector$.$

Let two vectors A and B are inclined to each other at angle θ.

★ Dot product of two vectors :

➝ A • B = |A| |B| cosθ = AB cosθ

★ Cross product of two vectors :

➝ A × B = |A| |B| sinθ = AB sinθ

ATQ, vector product and dot product are equal to each other.

∴ A • B = A × B

∴ AB cosθ = AB sinθ

∴ sinθ/cosθ = AB/AB = 1

• sinθ/cosθ = tanθ

∴ tanθ = 1

∴ θ = tan‾¹ (1)

∴ θ = 45° or π/4 rad