Miscellaneous

Misc 1
Important
You are here

Misc 2

Misc 3 Important

Misc 4

Misc 5 Important

Misc 6

Misc 7 Important

Misc 8 Important

Misc 9

Misc 10

Misc 11 Important

Misc 12 Important

Misc 13

Misc 14 Important

Misc 15 Important

Misc 16 (MCQ) Important

Misc 17 (MCQ) Important

Misc 18 (MCQ) Important

Misc 19 (MCQ) Important

Last updated at April 16, 2024 by Teachoo

Misc 1 Write down a unit vector in XY-plane, making an angle of 30Β° with the positive direction of x-axis.Let the unit vector be π β π β = π₯π Μ + yπ Μ + zπ Μ Since the vector is in XY plane, there is no Z βcoordinate. π β = xπ Μ + yπ Μ + 0π Μ π β = ππ Μ + yπ Μ Since π β makes an angle 30Β° with the xβaxis Also, Unit vector in direction of x axis is π Μ & in y axis is π Μ Angle with X-axis Since π β makes an angle of 30Β° with x-axis So, angle between π β & π Μ is 30Β° We know that, π β . π β = |π β ||π β | cos ΞΈ, Putting π β = π β , π β = π Μ & ΞΈ = ΞΈ 30Β° π β .π Μ = |π β ||π Μ | cos 30Β° π β .π Μ = 1 Γ 1 Γ cos 30Β° π β . π Μ = cos 30Β° (π₯π Μ + yπ Μ + 0π Μ). π Μ = cos 30Β° (π₯π Μ + yπ Μ + 0π Μ). (1π Μ + 0π Μ + 0π Μ) = cos 30Β° π₯.1 + y.0 + 0.0 = cos 30Β° (As π β is unit vector, |π β | = 1 & π Μ is a unit vector, |π Μ | = 1) x = cos 30Β° x = βπ/π Angle with Y-axis π β makes an angle of (90Β° β 30Β°) i.e. 60Β° with y-axis So, angle between π β & π Μ is 60Β° We know that, π β . π β = |π β ||π β | cos ΞΈ, Putting π β = π β , π β = π Μ & ΞΈ = 60Β° π β .π Μ = |π β ||π Μ | cos 60Β° π β .π Μ = 1 Γ 1 Γ cos 60Β° π β .π Μ = cos 60Β° (π₯π Μ + yπ Μ + 0π Μ). π Μ = cos 60Β° (π₯π Μ + yπ Μ + 0π Μ). (0π Μ + 1π Μ + 0π Μ) = cos 60Β° π₯.0 + y.1 + 0.0 = cos 60Β° y = cos 60Β° y = π/π Thus, π β = xπ Μ + yπ Μ π β = βπ/π π Μ + π/π π Μ