Practice portal › Motion in a Plane › Vector Addition and the Resultant

Which of the following relations is true for two unit vectors ̂A and ̂B making an angle θ to each other?

Asked in JEE Main 25th June 1st Shift 2022 · Vector subtraction

• (1) |̂A + ̂B| = |̂A - ̂B|tan θ/2
• (2) |̂A - ̂B| = |̂A + ̂B|tan θ/2
• (3) |̂A + ̂B| = |̂A - ̂B|cos θ/2
• (4) |̂A - ̂B| = |̂A + ̂B|cos θ/2

Step-by-step solution

Why the other options are wrong

• (1) Inverted: the sum is the difference times cot(θ/2), not tan(θ/2).
• (3) The ratio of the two magnitudes is tan(θ/2), not cos(θ/2).
• (4) The ratio of the two magnitudes is tan(θ/2), not cos(θ/2).

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.