web analytics

Misc 1 - Write down a unit vector in XY-plane, making angle 30 - Unit vector

Slide2.JPG
Slide3.JPGSlide4.JPG

  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
Ask Download

Transcript

Misc 1 Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of x-axis. Let the unit vector be 𝑎﷯ We know that 𝑎﷯ = 𝑥 𝑖﷯ + y 𝑗﷯ + z 𝑘﷯ Since the vector is in X-Y plane, there is no z– coordinate. Hence, 𝑎﷯ = x 𝑖﷯ + y 𝑗﷯ + 0 𝒌﷯ 𝒂﷯ = 𝒙 𝒊﷯ + y 𝒋﷯ Unit vector in direction of x axis is 𝑖﷯ & in y axis is 𝑗﷯ Given that 𝑎﷯ makes an angle of 30° with x-axis So, angle between 𝑎﷯ & 𝑖﷯ is 30° Now, we know that, 𝑎﷯ . 𝑏﷯ = 𝑎﷯﷯ 𝑏﷯﷯ cos θ, Putting 𝑎﷯ = 𝑎﷯ , 𝑏﷯ = 𝑖﷯ & θ = 30° 𝒂﷯ . 𝒊﷯ = 𝒂﷯﷯ 𝒊﷯﷯ cos 30° 𝑎﷯ . 𝑖﷯ = 1 × 1 × ﷮3﷯﷮2﷯ 𝑎﷯ . 𝑖﷯ = ﷮3﷯﷮2﷯ (𝑥 𝑖﷯ + y 𝑗﷯ + 0 𝑘﷯). 𝑖﷯ = ﷮3﷯﷮2﷯ (𝑥 𝑖﷯ + y 𝑗﷯ + 0 𝑘﷯). (1 𝑖﷯ + 0 𝑗﷯ + 0 𝑘﷯) = ﷮3﷯﷮2﷯ 𝑥.1 + y.0 + 0.0 = ﷮3﷯﷮2﷯ 𝒙= ﷮𝟑﷯﷮𝟐﷯ Similarly, 𝑎﷯ makes an angle of 60° with y-axis So, angle between 𝒂﷯ & 𝒋﷯ is 60° Now, we know that, 𝑎﷯ . 𝑏﷯ = 𝑎﷯﷯ 𝑏﷯﷯ cos θ, Putting 𝑎﷯ = 𝑎﷯ , 𝑏﷯ = 𝑗﷯ & θ = 60° 𝒂﷯ . 𝒋﷯ = 𝒂﷯﷯ 𝒋﷯﷯ cos 60° 𝑎﷯ . 𝑗﷯ = 1 × 1 × 1﷮2﷯ 𝑎﷯ . 𝑗﷯ = 1﷮2﷯ (𝑥 𝑖﷯ + y 𝑗﷯ + 0 𝑘﷯). 𝑗﷯ = 1﷮2﷯ (𝑥 𝑖﷯ + y 𝑗﷯ + 0 𝑘﷯). (0 𝑖﷯ + 1 𝑗﷯ + 0 𝑘﷯) = 1﷮2﷯ 𝑥.0 + y.1 + 0.0 = 1﷮2﷯ y = 𝟏﷮𝟐﷯ Thus, 𝑎﷯ = 𝑥 𝑖﷯ + y 𝑗﷯ = ﷮𝟑﷯﷮𝟐﷯ 𝒊﷯ + 𝟏﷮𝟐﷯ 𝒋﷯

About the Author

CA Maninder Singh's photo - Expert in Practical Accounts, Taxation and Efiling
CA Maninder Singh
CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .
Jail