Answer
Verified
417k+ views
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.
Complete step by step answer:
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 $
Also, the formula used for calculating the force acting on the vertical vector is given below
${F_y} = F\sin \theta $
Now, we can see that the direction of both the vectors can be calculated using the trigonometric function. Therefore, we can say that there is only one and one way in which a given vector can be resolved in given directions.Hence proved.
Note:Here, in the above question, the direction of the horizontal and vertical vectors can be calculated by using the cosine and sine of the angle between the vectors. Since both the cosine and sine are the trigonometric functions. That is why the method of resolving direction is the same.
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.
Complete step by step answer:
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 $
Also, the formula used for calculating the force acting on the vertical vector is given below
${F_y} = F\sin \theta $
Now, we can see that the direction of both the vectors can be calculated using the trigonometric function. Therefore, we can say that there is only one and one way in which a given vector can be resolved in given directions.Hence proved.
Note:Here, in the above question, the direction of the horizontal and vertical vectors can be calculated by using the cosine and sine of the angle between the vectors. Since both the cosine and sine are the trigonometric functions. That is why the method of resolving direction is the same.
Recently Updated Pages
Who among the following was the religious guru of class 7 social science CBSE
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Trending doubts
Derive an expression for drift velocity of free electrons class 12 physics CBSE
Which are the Top 10 Largest Countries of the World?
Write down 5 differences between Ntype and Ptype s class 11 physics CBSE
The energy of a charged conductor is given by the expression class 12 physics CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Derive an expression for electric field intensity due class 12 physics CBSE
How do you graph the function fx 4x class 9 maths CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Derive an expression for electric potential at point class 12 physics CBSE