NCERT solution Class 11 motion in a plane

NCERT Solutions

Class 11 Physics

Motion in a Plane

NCERT Questions

Q. 3.1
Q. 3.2
Q. 3.3
Q. 3.4
Q. 3.5
Q. 3.6
Q. 3.7
Q. 3.8
Q. 3.9
Q. 3.10
Q. 3.11
Q. 3.12
Q. 3.13
Q. 3.14
Q. 3.15
Q. 3.16
Q. 3.17
Q. 3.18
Q. 3.19
Q. 3.20
Q. 3.21
Q. 3.22

Q. 3.19

î and ĵ are unit vectors along x- and y- axis respectively. What is the magnitude and direction of the vectors î + ĵ and î - ĵ? What are the components of a vector A= 2 î + 3 ĵ along the directions of (î + ĵ) and (î - ĵ)? [You may use graphical method]

Magnitude of (î + ĵ) = | î + ĵ|

=√ (1)² + (1)² = √2

Let the vector (î + ĵ) make an angle θ with the direction of î, then

cos θ = ( (î + ĵ). Î)/ (| î + ĵ|| î|

= (1/√2) = cos 45⁰ or θ = √2

Magnitude of (î - ĵ) = | î - ĵ|

=√ (1)² + (-1)² = √2

Similarly, if vector (î - ĵ) makes an angle θ with the direction of î, then

cos θ = ((î - ĵ). Î)/ (| î - ĵ|. Ĵ)

= (1/√2) (1)

= (1/√2)

cos 45⁰ or θ =45⁰

Here θ = -45⁰ with x-axis.

Given :- A = 2 î + 3 ĵ

A_x î + A_y ĵ = 2 î + 3 ĵ

On Comparing: - A_x = 2 and A_y = 3

| A| =√ (2)² + (3)²

=√13

Let A_x make an angle θ with the x-axis, as shown in the following figure.

Therefore, tan θ = (A_x/A_y)

θ = tan^-1(3/2)

=tan^-1(1.5) = 56.31⁰

Angle between the vectors (2 î + 3 ĵ) and (î + ĵ),

θ = (56.31⁰ – 45⁰) = 11.31⁰

Component of vector A, along the direction of P, making and angle θ

= (A cos θ) P

= (A cos11.31) (î + ĵ)/ (√2)

= √13 x (0.9806) (î + ĵ) / (√2)

=2.5 (î + ĵ)

= (25/10) x (√2)

= (5/ (√2))

Let θ be the angle between the vector :( 2 î + 3 ĵ) and (î - ĵ),

θ = (45⁰ +56.31⁰) = 101.31⁰

Component of vector A, along the direction of Q, making and angle θ.

= (A cos θ) Q

= (A cos θ) (î – ĵ)/ (√2)

= (√13) cos (901.31⁰) (î – ĵ)/ (√2)

= (√13)/ (√2) sin (11.30⁰) (î – ĵ)

=-2.550 x 0.196(î – ĵ)

=-0.5(î – ĵ)

=-(5/10) x (√2)

=-(1/ (√2))

Video solution:

Motion in a Plane Class 11 Physics NCERT Chapter 3 NCERT Solutions

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