`phi = arcsin( v_y / |vecv| )`

Enter a value for all fields

The Vector Angle equation computes the angle, `phi`, of a vector from the magnitude of the angle, |`vecv`| and the y-component of the vector, v_y. See Figure B.

INSTRUCTIONS: Enter the following:

• (|`vecv`| ) Vector Magnitude
• (v_y) Vertical Vector Component

Vector Angle (`phi`): The calculator returns the angle in degrees.  However, this can be automatically converted to compatible units via the pull-down menu.

3D Vector Functions

• k V - scalar multiplication
• V / |V| - Computes the Unit Vector
• |V| - Computes the magnitude of a vector
• U + V - Vector addition
• U - V - Vector subtraction
• |U - V| - Distance between vector endpoints.
• |U + V| - Magnitude of vector sum.
• V • U - Computes the dot product of two vectors
• V x U - Computes the cross product of two vectors
• Vector Angle - Computes the angle between two vectors
• Vector Projection - Compute the vector projection of V onto U.
• Area between Vectors - Computes the area between two vectors
• Vector Rotation - Compute the result vector after rotating around an axis.
• (ρ, θ, φ) to (x,y,z) - Spherical to Cartesian coordinates
• (x,y,z) to (ρ, θ, φ) - Cartesian to Spherical coordinates
• (r, θ, z) to (x,y,z) - Cylindrical to Cartesian coordinates
• (x,y,z) to (r, θ, z) - Cartesian to Cylindrical coordinates

Reference

Young, Hugh and Freeman, Roger.  University Physics With Modern Physics.  Addison-Wesley, 2008. 12th Edition, (ISBN-13: 978-0321500625 ISBN-10: 0321500628 ) Pg 16 eq 1.6