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# Prove that there is only one and one way in which a given vector can be resolved in given directions.

Last updated date: 07th Aug 2024
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Hint: Vector can be defined as a physical quantity that has both magnitude and direction. Also, a vector is a physical quantity that can be represented as a straight line with an arrow head. The formula used for proving the statement is given below.

Formula used:
The formula used for calculating the force acting on the horizontal vector is given below
${F_x} = F\cos \theta$
Here, ${F_x}$ is the force acting on the horizontal component, $F$ is the force on vectors and $\theta$ is the angle between the vectors.
Also, the formula used for calculating the force acting on the vertical vector is given below
${F_y} = F\sin \theta$
Here, ${F_y}$ is the force acting on the vertical component, $F$ is the force on vectors and $\theta$ is the angle between the vectors.

Let us consider a vector $A$. Let this vector have two components from which one will be along the horizontal axis and the other will be along the vertical axis. Now, the formula used for calculating the force acting on the horizontal vector is given below
${F_x} = F\cos \theta$
${F_y} = F\sin \theta$