# Math Assignment Help With Angle Between Two Vectors

## 2.7.2.2 Angle between two vectors:

Let the coordinates of any two nonzero vectors u and v. The angle q between them:

u = ai + bj + ck
v = xi + yj + zk
u.v = u v cos q
u.v = a x + b y + c z

therefore, u v cos q = a x + b y + c z

q = cos-1 o (a x + b y + c z) / ( u v ) p

### 2.7.2.3 Cross Product:

The vector product of two vectors A and B, also called the cross product, is denoted by A X B.

The symbol used to represent cross product is a cross (×). Since this product has both, magnitude and direction, it is also known as the vector product.

A × B = AB sin θ ˆn

The vector ˆn ("n hat") is a unit vector perpendicular to the plane formed by the two vectors. The direction of ˆn is determined by the right hand rule.

The cross product is distributive i.e.

A × (B + C) = (A × B) + (A × C)

but not commutative i.e.

A × B = −B × A

On reversing the order of cross multiplication the direction of the product also get reversed

If we know the components of A and B, we can calculate the components of the vector product, using a procedure similar to that for the scalar product.

The components of

C = A X B

are given by

Cx = Ax + Bx,

Cy = Ay + By,

Cz = Az + Bz

The cross product of any vector with itself is zero .i.e.

A × A = 0

Applying this corollary to the unit vectors means that the cross product of any unit vector with itself is zero.

î × î = ĵ × ĵ = ˆk × ˆk = (1)(1)(sin 0°) = 0

It should be noted that the cross product of any unit vector with other will give a magnitude of one, because

sine90° = 1

The right hand rule for cross multiplication relates the direction of the two vectors with the direction of their product. Since cross multiplication is not commutative.