NCERT Class 11 Physics Solutions: Chapter 4 – Motion in a Plane Part 9

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Question 4.22:

Are unit vectors along x and y-axis respectively. What is the magnitude and direction of the vectors and ? What are the components of a vector along the directions of ? [You may use graphical method]

Answer:

Consider a vector , given as:

On comparing the components on both sides, we get:

Hence, the magnitude of the vector is .

Let be the angle made by the vector, with the x-axis, as shown in the following figure:

Figure shown angle due to vector P

Figure 4.22 Angle Made by Vector P

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Hence , The Vector makes an angle of with the x-axis.

Let,

Hence, the magnitude of the vector is

Let be the angle made by the vector , with the x-axis, as shown in the following figure:

Figure shown the θ angle by vector Q.

Figure 4.22 Angle Made by Vector Q

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Hence, the vector makes an angle of with the x-axis.

It is given that:

On comparing the coefficients of, we have:

And

Let make an angle with the x-axis, as shown in the following figure:

Figure shown (A x ) make an angle with the x-axis.

Figure 4.22 Angle Made by Vector A

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Angle between the vectors and ,

Component of vector , along the direction of , making an angle ,

Let be the angle between the vectors and

Component of vector , along the direction of, making an angle,