Last updated at May 29, 2018 by Teachoo

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 × 32 𝑎 . 𝑖 = 32 (𝑥 𝑖 + y 𝑗 + 0 𝑘). 𝑖 = 32 (𝑥 𝑖 + y 𝑗 + 0 𝑘). (1 𝑖 + 0 𝑗 + 0 𝑘) = 32 𝑥.1 + y.0 + 0.0 = 32 𝒙= 𝟑𝟐 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 × 12 𝑎 . 𝑗 = 12 (𝑥 𝑖 + y 𝑗 + 0 𝑘). 𝑗 = 12 (𝑥 𝑖 + y 𝑗 + 0 𝑘). (0 𝑖 + 1 𝑗 + 0 𝑘) = 12 𝑥.0 + y.1 + 0.0 = 12 y = 𝟏𝟐 Thus, 𝑎 = 𝑥 𝑖 + y 𝑗 = 𝟑𝟐 𝒊 + 𝟏𝟐 𝒋

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.