How may the resultant of two vectors be computed analytically from a vector parallelogram?

The resultant of two vectors is calculated by the formula R^2=P^2+Q^2+2PQcosΘ

The resultant of two vectors can be calculated by the vector parallelogram method, in which basic property of trigonometry is used to setup a simple formula for the resultant of two vectors.

Consider two vector P and Q, making an angle Θ from each other.

From right angled triangle  OCD

OC^2=OD^2+DC^2

R^2=(OA+AD)^2+DC^2

R^2=OA^2+AD^2+2OA*AD+DC^2

From triangle ADC

AC^2=AD^2+CD^2, and cos Θ=AD/AC

R^2=OA^2+AC^2+2OA*AC*cosΘ

R^2=P^2+Q^2+2PQcosΘ

speed

ratio of distance traveled to time interval

net force

vector sum of forces on object

object

source of diverging light rays either luminous or illuminated

don't remove my answer im trying my best to answer them

explanation: