Vector Cross Product and Applications

|\vec{A} \times \vec{B}|

|\vec{A} + \vec{B}|

|\vec{A}| \times |\vec{B}|

|\vec{A} + \vec{B}|

\vec{\tau} = \vec{r} \times \vec{F}

\vec{\tau} = \vec{F} \times \vec{r}

(1/√3)(x̂-ĵ+k̂)

(1/√2)(x̂+ĵ)

(1/√6)(2x̂+3ĵ-5k̂)

(1/2)(x̂+k̂)

The gradient of a scalar function φ(x, y, z) is defined as ∇φ = i ∂φ/∂x + j ∂φ/∂y + k ∂φ/∂z.

The gradient of a scalar function φ(x, y, z) is defined as ∇φ = i ∂φ/∂y + j ∂φ/∂z + k ∂φ/∂x.

The gradient of a scalar function φ(x, y, z) is defined as ∇φ = i ∂φ/∂z + j ∂φ/∂x + k ∂φ/∂y.

The gradient of a scalar function φ(x, y, z) is defined as ∇φ = i φ + j φ + k φ.

Vector

Scalar

True

False

The divergence of a vector A⃗ is defined as div A⃗ = ∇·A⃗ = ∂A_x/∂x + ∂A_y/∂y + ∂A_z/∂z.

The divergence of a vector A⃗ is defined as div A⃗ = ∇×A⃗ = ∂A_x/∂y + ∂A_y/∂z + ∂A_z/∂x.

The divergence of a vector A⃗ is defined as div A⃗ = ∇·A⃗ = ∂A_x/∂y + ∂A_y/∂z + ∂A_z/∂x.

The divergence of a vector A⃗ is defined as div A⃗ = ∇·A⃗ = ∂A_x/∂z + ∂A_y/∂x + ∂A_z/∂y.

True

False