Misc 17 - Chapter 10 Class 12 Vector Algebra

Transcript

Misc 17 Let and be two unit vectors and is the angle between them. Then + is a unit vector if (A) = 4 (B) = 3 (C) = 2 (D) = 2 3 Given & are unit vectors, So, = 1 & = 1 We need to find if + is a unit vector Therefore, + =1 + = 1 2 + . + = 1 . + + . + = 1 . + . + . + . = 1 + . + . + =1 12 + . + . + 12 = 1 2 + . + . = 1 2 + . + . = 1 2 + 2 . = 1 2 . = 1 2 . = 1 2 cos = 1 2 1 1 cos = 1 2 cos = We know that cos 60° = 1/2 & cos is negative in 2nd quadrant, So, θ = 180 − 60° θ = 120° θ = 120 × 𝜋/180 θ = 2𝜋/3 So θ = 2𝜋/3 Hence, option (D) is correct