Angle Between Equal Vector

Since Equal vector always have same magnitude and direction so angle between two equal vectors must be zero, this can be proved using the dot product of two vectors. Let two Equal Vectors A = xi + yj + zk and B = xi + yj + zk such that angle between them is θ.

So,

A.B (A dot B ) = |A| |B| Cosθ

where,

• A.B = (xi + yj + zk ). (xi + yj + zk ) = x² + y²+ z²
• |A| = √x² + y² + z²
• |B| = √x² + y² + z²

So,

Cos θ = A.B / |A| |B|

= x² + y² + z² / (√x² + y² + z²)(√x² + y² + z²)

= 1

θ = 0°

Equal Vectors have equal length and the same Unit Vector. Two Vectors are said to be equal when they have the same magnitude and when they are acting in the same direction. Equal Vectors play an important role in Mathematics and Physics; they are used for simplifying complex problems, shifting coordinates, or finding errors in complex algorithm problems.

In this article, we will learn what vectors are, what equal vectors are, the properties of equal vectors, the angle between equal vectors, the application of Equal Vectors, and many more details.